Banks/BHC/T&L/CRA Market Risk April 2018 Chapter 9 - Page 1 Guideline Subject: Capital Adequacy Requirements (CAR) Chapter 9 – Market Risk Effective Date: April 2018 The Capital Adequacy Requirements (CAR) for banks (including federal credit unions), bank holding companies, federally regulated trust companies, federally regulated loan companies and cooperative retail associations are set out in nine chapters, each of which has been issued as a separate document. This document, Chapter 9 – Market Risk, should be read in conjunction with the other CAR chapters which include: Chapter 1 Overview Chapter 2 Definition of Capital Chapter 3 Credit Risk – Standardized Approach Chapter 4 Settlement and Counterparty Risk Chapter 5 Credit Risk Mitigation Chapter 6 Credit Risk- Internal Ratings Based Approach Chapter 7 Structured Credit Products Chapter 8 Operational Risk Chapter 9 Market Risk Please refer to OSFI’s Corporate Governance Guideline for OSFI’s expectations of institution Boards of Directors in regards to the management of capital and liquidity.
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Banks/BHC/T&L/CRA Market Risk
April 2018 Chapter 9 - Page 1
Guideline Subject: Capital Adequacy Requirements (CAR)
Chapter 9 – Market Risk
Effective Date: April 2018
The Capital Adequacy Requirements (CAR) for banks (including federal credit unions), bank
operational risks, early termination, investing and funding costs, and future administrative costs
and, where appropriate, model risk. [BCBS June 2006 par 699, revised December 2010
par 718(cix)]
9.8.4 Adjustment to the current valuation of less liquid positions for regulatory capital
purposes
43. Institutions must establish and maintain procedures for judging the necessity of and
calculating an adjustment to the current valuation of less liquid positions for regulatory capital
purposes. This adjustment may be in addition to any changes to the value of the position required
for financial reporting purposes and should be designed to reflect the illiquidity of the position.
OSFI expects institutions to consider the need for an adjustment to a position’s valuation to
reflect current illiquidity whether the position is marked to market using market prices or
observable inputs, third-party valuations or marked to model. [BCBS December 2010 par
718(cx)]
44. Bearing in mind that the assumptions made about liquidity in the market risk capital
charge may not be consistent with the institution’s ability to sell or hedge out less liquid
positions where appropriate, institutions must take an adjustment to the current valuation of these
positions, and review their continued appropriateness on an on-going basis. Reduced liquidity
may have arisen from market events. Additionally, close-out prices for concentrated positions
and/or stale positions should be considered in establishing the adjustment. Institutions must
consider all relevant factors when determining the appropriateness of the adjustment for less
liquid positions. These factors may include, but are not limited to, the amount of time it would
take to hedge out the position/risks within the position, the average volatility of bid/offer spreads,
the availability of independent market quotes (number and identity of market makers), the
average and volatility of trading volumes (including trading volumes during periods of market
stress), market concentrations, the aging of positions, the extent to which valuation relies on
marking-to-model, and the impact of other model risks not included in the prior paragraph.
[BCBS June 2006 par 700, revised December 2010 par 718(cxi)]
45. For complex products including, but not limited to, securitization exposures and n-th-to-
default credit derivatives, institutions must explicitly assess the need for valuation adjustments to
reflect two forms of model risk: the model risk associated with using a possibly incorrect
valuation methodology; and the risk associated with using unobservable (and possibly incorrect)
calibration parameters in the valuation model. [BCBS December 2010 par 718(xci-1-)]
46. The adjustments to the current valuation of less liquid positions made under the
previous two paragraphs must impact Common Equity Tier 1 regulatory capital and may exceed
those valuation adjustments made under financial reporting standards and those considered in
Section 9.8.3. [BCBS June 2006 par 701, revised December 2010 par 718(cxii)]
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April 2018 Chapter 9 - Page 15
9.9. Capital requirement
47. Each institution will be expected to monitor and report the level of risk against which a
capital requirement is to be applied. The institution's total capital requirement for market risk
will be:
a. the sum of the capital charges for market risks as determined using the standardized
approach or
b. the measure of market risk derived from the models approach or
c. a mixture of (a) and (b) summed arithmetically.
[BCBS June 2006 par 701(v)]
48. All transactions, including forward sales and purchases, shall be included in the
calculation of capital requirements on a trade date basis. Although regular reporting will take
place only quarterly, institutions are expected to manage risks in such a way that the capital
requirements are being met on a continuous basis, i.e., at the close of each business day.
Institutions are also expected to maintain strict risk management systems to ensure that intra-day
exposures are not excessive. [BCBS June 2006 par 701(vi)]
Appendix 9-1 - Summary of Capital Charges by Instrument
49. The following tables have been provided for illustrative purposes and are intended to
give a broad indication of the capital charges that apply to selected instruments. Specific
instruments may be subject to additional charges: For example, a debt instrument denominated
in a foreign currency and held in the trading book would be subject to both the general market
risk charge for interest rate position risk and foreign exchange risk. The same debt instrument
held outside the trading book would be subject to a general market risk charge for foreign
exchange and a credit default risk charge.
Instruments Specific
Risk Charge
General Market
Risk Charge
Options Risk
Charge
Credit Default
Risk Charge4
Interest rate position risk
Debt instruments5 X X
Debt forward contracts X X X
Debt index forward contracts X X
Equity position risk
Equity instruments X X
Equity forward contracts X X X
4 Exchange traded contracts subject to daily margining requirements may be excluded from the capital calculation. 5 This refers only to trading book instruments.
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April 2018 Chapter 9 - Page 16
Instruments Specific
Risk Charge
General Market
Risk Charge
Options Risk
Charge
Credit Default
Risk Charge4
Equity index forward contracts X6 X X
Foreign exchange position
risk
Foreign exchange spot X X
Foreign exchange forward X X
Commodities risk
Gold spot X X
Gold forward contracts X X
Commodity spot X X
Commodity forward contracts X X
Instruments Specific
Risk Charge
General Market
Risk Charge
Options Risk
Charge
Credit Default
Risk Charge
Options Portfolios
Simplified Method
Debt options purchased X X
Debt index options purchased X X
Equity options purchased X X
Equity index options purchased X X
Foreign exchange options
purchased X X
Gold options purchased X X
Commodity options purchased X X
Scenario Method
Debt options X X X
Debt index options X X
Equity options X X X
Equity index options X7 X X
6 Diversified equity indices require a low specific risk charge of 2% to cover execution and tracking risks. 7 Diversified equity indices require a low specific risk charge of 2% (multiplied by the notional value of the
underlying and the option's delta as set out on section 8.10.5) to cover execution and tracking risks.
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April 2018 Chapter 9 - Page 17
Instruments Specific
Risk Charge
General Market
Risk Charge
Options Risk
Charge
Credit Default
Risk Charge
Foreign exchange options X X
Gold options X X
Commodity options X X
9.10. Standardized approach
9.10.1. Interest rate position risk
50. This section describes the way in which an institution will calculate its capital
requirement for interest rate positions held in the trading book where that institution does not use
an internal model that meets the criteria set out in section 9.11. The interest rate exposure
captured includes exposures arising from interest-bearing and discounted financial instruments,
derivatives based on the movement of interest rates and interest rate exposures embedded in
derivatives based on non-interest related derivatives including foreign exchange forward
contracts. The market risk capital charge for interest rate options in an institution's trading book
is calculated separately in accordance with section 9.10.5.
51. Convertible bonds, i.e., debt instruments or preference shares that are convertible, at a
stated price, into common shares of the issuer, will be treated as debt securities if they trade like
debt securities and as equities if they trade like equities. [BCBS June 2006 par 709(i)]
Convertible bonds must be treated as equities where:
a. the first date at which conversion may take place is less than three months ahead, or the
next such date (where the first has passed) is less than a year ahead; and
b. the convertible is trading at a premium of less than 10%, where the premium is defined as
the current mark to market value of the convertible less the mark to market value of the
underlying equity, expressed as a percentage of the mark to market value of the
underlying equity.
52. An institution's interest rate position risk requirement under the standardized approach
is the sum of the capital required for specific risk and general market risk for each currency in
which the institution has a trading book exposure. The specific risk capital charge depends on the
type of product. [BCBS June 2006 par 709(ii)]
9.10.1.1 Specific risk
Non-tranched products
53. The treatment for products that are not covered under the securitization framework (as
defined in Chapter 7 – Structured Credit Products, section 7.1), and that are not n-th-to-default
products, is as follows:
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April 2018 Chapter 9 - Page 18
54. The specific risk capital charge is calculated by multiplying the absolute market values
of the net positions in the trading book by their respective risk factors. The risk factors, as set
out below in Table I, correspond to the category of the obligor and the residual maturity of the
instrument.
55. Net positions are arrived at by applying permitted offsets of long and short positions in
identical issues (including certain derivative contracts – see sub-section in 9.10.1.1. ). Even if
the issuer is the same, no offsetting is permitted between different issues to arrive at a net
holding since differences in currencies, coupon rates, liquidity, call features, etc., mean that
prices may diverge in the short run. [BCBS June 2006 par 709(iii)]
TABLE I [BCBS June 2006 par 710]
Specific Risk Categories and Weights
Category External Credit
Assessment
Residual Term to Final
Maturity
Specific Risk
Capital Charge
Government
AAA to AA- All 0%
A+ to BBB-
6 months or less 0.25%
Greater than 6 months but not
exceeding 24 months 1.00%
Greater than 24 months 1.60%
BB+ to B- All 8.00%
Below B- All 12.00%
Unrated All 8.00%
Qualifying All
6 months or less 0.25%
Greater than 6 months but not
exceeding 24 months 1.00%
Greater than 24 months 1.60%
Other
Similar to credit risk charges under the standardized approach for non-
investment grade debt securities, e.g.:
BB+ to BB- All 8.00%
Below BB- All 12.00%
Unrated All 8.00%
OSFI Notes
56. The treatment of a sovereign asset under the standardized approach to specific risk is
based on its rating. Obligations of Canadian provinces are treated as obligations of the
government of Canada for the purpose of specific risk factors in the framework.
57. A specific risk charge will apply to derivative contracts in the trading book only when
they are based on an underlying instrument. For example, where an interest rate swap is based
on an index of Bankers’ Acceptance rates, there will not be a specific risk charge. However an
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April 2018 Chapter 9 - Page 19
option based on a corporate bond will generate a specific risk charge. Appendix 9-V includes
examples of derivatives in the trading book that require a specific risk charge and derivatives in
the trading book that do not.
58. The specific risk charge for net positions in derivative contracts is calculated by
multiplying:
The market value of the effective notional amount of the debt instrument that underlies an
interest rate swap, future or forward
by
the specific risk factors in Table I that correspond to the category and residual term of the
underlying debt instrument.
Effective notional amount
59. The effective notional amount of a derivative net position is the (absolute) market value
of a net position in a stated underlying debt instrument adjusted to reflect any multiplier
applicable to the contract's reference rate(s) or, where there is no multiplier component, simply,
the market value of the stated underlying debt instrument.
60. All over-the-counter derivative contracts are subject to the counterparty credit risk
charges determined in accordance with Chapter 5 – Credit Risk Mitigation, even where a specific
risk charge is required. A specific risk requirement would arise if the derivative position was
based on an underlying instrument or security. For example, if the underlying security was a
AAA rated corporate bond, the derivative will attract a specific risk requirement based on the
underlying bond. However, where the derivative was based on an underlying exposure that was
an index (e.g., interbank rates), no specific risk would arise.
Government
61. The government category includes all forms of debt instruments, including but not
limited to bonds, treasury bills and other short-term instruments, that have been issued by, fully
guaranteed by, or fully collateralized by securities issued by:
the Government of Canada, or the government of a Canadian province or territory; or
an agent of the federal government, or a provincial or territorial government in Canada
whose debts are, by virtue of their enabling legislation, direct obligations of the parent
government.
[BCBS June 2006 par 710(i)]
62. The government category also includes all forms of debt instruments that are issued by,
or fully guaranteed by, central governments that:
have been rated, and whose rating is reflective of the issuing country’s creditworthiness;
or
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April 2018 Chapter 9 - Page 20
are denominated in the local currency of the issuing government, and funded by liabilities
booked in that currency.
[BCBS June 2006 par 711]
Qualifying
63. The qualifying category includes debt securities that are rated investment-grade and
issued by or fully guaranteed by:
a. a public sector entity,
b. a multilateral development bank8,
c. a bank where the instrument does not qualify as capital of the issuing institution9, or
d. a regulated securities firm in a BCBS-member country or country that has implemented
BCBS-equivalent standards.
[BCBS June 2006 par 711(i)]
OSFI Notes
64. OSFI expects the institution to conduct its own internal self-assessment as to whether a
non-BCBS member country has implemented BCBS equivalent standards.
65. In addition, the qualifying category also includes any other debt securities issued by a
non-government obligor that have been rated investment-grade10 by at least two nationally
recognized credit rating services, or rated investment-grade by one nationally recognized credit
rating agency and not less than investment-grade by any other credit rating agency. [BCBS June
2006 par 711(ii)]
66. Furthermore, institutions using the IRB approach for a portfolio may include an unrated
security in the qualifying category if the security meets both of the following conditions:
a. the security is rated equivalent to investment grade under the institution’s internal rating
system11, which OSFI has confirmed complies with the requirements for the IRB
approach, and
b. the issuer has securities listed on a recognized stock exchange.
[BCBS June 2006 par 712]
8 Multilateral banks are defined in Chapter 3 – Credit Risk – Standardized Approach. 9 Government-sponsored agencies, multilateral development banks, and banks are defined in Chapter 3 – Credit
Risk – Standardized Approach. Instruments issued by banks should meet the ratings criteria listed in paragraph
65 and should originate from a BCBS-member country or country that has implemented BCBS-equivalent
standards . 10 See Table II below - e.g., rated Baa or higher by Moody’s and BBB or higher by Standard and Poor’s.. 11 Equivalent means that the debt security has a one-year PD less than or equal to the one year PD implied by the
long-run average one-year PD of a security rated investment grade or better by a nationally recognized rating
agency.
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67. Nationally recognized credit rating agencies include but are not restricted to:
a. DBRS,
b. Moody's Investors Service (Moody's),
c. Standard & Poors (S&P),
d. Fitch Rating Services (Fitch),
e. Japan Credit Rating Agency, LTD (JCR), and
f. Japan Rating and Investment Information (R&I).
Table II provides the minimum ratings constituting investment grade for the agencies listed
above.
TABLE II
Example Minimum Ratings Comprising Investment Grade
Minimum Ratings
Rating Agency Securities Money market
DBRS BBB low A-3
Moody's Baa3 P-3
S&P BBB- A-3
Fitch BBB- A-3
JCR BBB- J-2
R&I BBB- a-3
Other
68. The other category is comprised of securities that do not meet the criteria for inclusion
in the government or qualifying categories. Instruments in this category receive the same
specific risk charge as do non-investment grade securities under the standardized approach to
credit risk in this guideline. [BCBS June 2006 par 712(i)]
69. However, since this may in certain cases considerably underestimate the specific risk
for debt instruments that have a high yield to redemption relative to government debt securities,
OSFI will have the discretion:
To apply a higher specific risk charge to such instruments; and/or
To disallow offsetting for the purposes of defining the extent of general market risk
between such instruments and any other debt instruments.
[BCBS December 2010 par 712(ii)]
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Credit derivatives
70. This section describes the minimum capital required to cover specific risk for positions
in credit derivatives in the trading book. Such positions are also subject to the capital
requirements for counterparty credit risk.
For the purpose of calculating the capital requirement, credit derivatives transactions are broken
down into constituent components as follows.
Total rate of return swaps are represented as two legs of a single transaction. The first leg is
an effective notional position in the reference asset to which the corresponding general and
specific risk charges apply. The second leg, representing interest payments under the swap,
is recorded as a notional position in a government bond in the reference currency with the
appropriate fixed or floating rate.
Credit default swaps/products for the guarantor are represented as an effective notional
position in the reference asset but are subject only to a specific risk charge. For such
products, there is no general market risk position created in the reference asset. If periodic
premium or interest payments are required of the beneficiary under the swap, these cash
flows are represented as a notional position in a government bond in the reference currency
with the appropriate fixed or floating rate.
Credit-linked notes are treated as a position in the note itself, with an embedded credit default
product. The credit-linked note has specific risk of the issuer and general market risk
according to the coupon or interest rate of the note. The embedded credit default product
creates an effective notional position in the specific risk of the reference asset.
71. In almost all credit derivatives (including total rate of return swaps, credit default
products and credit-linked notes), specific risk is created in the reference asset. When the credit
derivative is for a single reference asset, the beneficiary creates a short position in the reference
asset, while the guarantor creates a long position in the reference asset. For some credit-linked
note products, or other products in which the guarantor funds the beneficiary (posts cash or
collateral), a long specific risk position in the note issuer, in the amount of the collateral, is also
created.
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Appendix 9-2 - Summary of Capital Charges for Credit Derivatives
72. The following table summarizes the application of capital charge components to the
73. The specific risk capital charge is calculated by multiplying the absolute values of the
derivative positions (mark-to-market) in the trading book by their respective risk factors, as
outlined elsewhere in this guideline. Institutions will generally use the factors in the non-
tranched products sub-section of 9.10.1.1.– Table I (Specific Risk Categories and Weights),
taking into account the category (government, qualifying, or non-qualifying) and the residual
maturity (six months to two years).
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Limitation of the specific risk capital charge to the maximum possible loss
74. Institutions may limit the capital charge for an individual position in a credit derivative
(or securitization instruments as described below in the tranched products sub-section of
9.10.1.1.) to the maximum possible loss. For a short risk position (beneficiary) this limit could be
calculated as a change in value due to the underlying names immediately becoming default risk-
free. For a long risk position (guarantor), the maximum possible loss could be calculated as the
change in value in the event that all the underlying names were to default with zero recoveries.
The maximum possible loss must be calculated for each individual position. [BCBS December
2010 par 712(viii)]
Netting
75. Netting of positions within the specific risk category is permitted under the conditions
described below. Where a credit default product or credit-linked note is of shorter maturity than
the reference asset, a specific risk offset is allowed between the long and short specific risk
positions, but a forward position in the specific risk of the reference asset is recorded. The net
result is a single specific risk charge for the longer maturity position in the reference asset.
76. No capital is required for specific risk for either side of a position in cases where the
values of the two legs (i.e., long and short) always move in the opposite direction and broadly to
the same extent. This occurs where:
a. the two legs consist of completely identical instruments12, or
b. a long cash position is hedged by a total rate of return swap (or vice versa) and there is an
exact match between the reference obligation and the underlying exposure (i.e., the cash
position).
[BCBS June 2006 par 713]
77. A partial reduction in the specific risk charge is permitted when the values of two legs
(i.e., long and short) always move in the opposite direction but not broadly to the same extent.
This occurs where a long cash position is hedged by a credit default swap or a credit linked note
(or vice versa) and there is an exact match in terms of the reference obligation, the maturity of
both the reference obligation and the credit derivative, and the currency to the underlying
exposure. In addition, the key features of the credit derivative contract (e.g., credit event
definitions, settlement mechanisms) do not cause the price movement of the credit derivative to
materially deviate from the price movements of the cash position.
78. To the extent that a transaction meeting the requirements of this paragraph transfers risk
(i.e., taking account of restrictive payout provisions such as fixed payouts and materiality
thresholds), the specific risk charge for the side of the transaction with the higher charge is
reduced by 80%, while the specific risk charge for the other side of the transaction is zero.
[BCBS June 2006 par 714]
12 The maturity of the swap itself may be different from that of the underlying exposure.
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79. A partial reduction in the specific risk charge is also permitted when the values of two legs
(i.e., long and short) usually move in the opposite direction. This occurs where:
The position is captured under b) above, with the exception that there is an asset
mismatch between the reference obligation and the underlying exposure. However, the
reference obligation ranks pari passu with or is junior to the underlying obligation, the
underlying and reference obligations share the same obligor (i.e., the same legal entity),
and there are legally enforceable cross-default or cross-acceleration clauses in place.
The position is captured under a) or paragraph 77 above, with the exception that there is a
currency or maturity mismatch13 between the credit protection and the underlying asset.
The position is captured under paragraph 77 above, with the exception that there is an
asset mismatch between the cash position and the credit derivative. However, the
underlying asset is included in the (deliverable) obligations in the credit derivative
documentation.
[BCBS June 2006 par 715]
80. In each of the above cases, the specific risk charge for the side of the transaction with
the higher charge remains the same, but the specific risk charge for the other side of the
transaction is zero. [BCBS June 2006 par 716]
81. For all other cases not specifically mentioned above, the full specific risk capital charge
applies to both sides of the position. [BCBS June 2006 par 717]
Tranched products
82. Tranched products include those covered under the securitization framework (as defined
in Chapter 7 - Structured Credit Products, section 7.1) and n-th to default products (henceforth
‘tranched products’). The specific risk charge for a tranched product depends on whether it is
eligible for inclusion in a correlation trading portfolio. Notwithstanding this eligibility, the rules
for permissible offsets as applied to non-tranched products (e.g., offsetting of long and short
positions is permitted for tranched positions only in identical issues) apply here as well. The
specific risk capital charge for a net position in a tranched product is calculated as the lesser of:
a. the product of the market value of the tranched product position and its respective charge
(outlined in Tables III and IV below);
and
b. the maximum possible loss that could arise under that net position.
83. Similar concepts apply if an institution is applying alternative (instead of the Ratings
Based Approach) treatments to unrated securitizations as described in the non-correlation trading
portfolio products sub-section of 9.10.1.1.
13 Currency mismatches should feed into the normal reporting of foreign exchange risk.
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OSFI Notes
84. Asset backed securities that do not involve “at least two different stratified risk
positions or tranches reflecting different degrees of credit risk” but might involve other sorts of
tranching associated with pre-payment, as an example, are not considered tranched products
under this framework. As a consequence, such products can be treated as non-tranched positions
for the purposes of specific risk capital requirements based on either the standardized framework
or internal models.
Correlation trading portfolio products
85. For the purposes of this framework, the correlation trading portfolio incorporates
securitization exposures and n-th-to-default credit derivatives that meet the following criteria:
a. The positions are neither securitization positions, nor derivatives of securitization
exposures that do not provide a pro-rata share in the proceeds of a securitization tranche
(this therefore excludes options on a securitization tranche, or a synthetically leveraged
super-senior tranche or any complex “double leverage” position that might not be
captured by the definition of re-securitization and therefore excluded.);
and
b. All reference entities are single-name products, including single-name credit derivatives,
for which a liquid two-way market exists. This will include commonly traded indices
based on these reference entities. A two-way market is deemed to exist where there are
independent bona fide offers to buy and sell so that a price reasonably related to the last
sales price or current bona fide competitive bid and offer quotations can be determined
within one day and settled at such price within a relatively short time conforming to trade
custom. Positions which reference an underlying that would be treated as a retail
exposure, a residential mortgage exposure or a commercial mortgage exposure under the
standardized approach to credit risk are not included in the correlation trading portfolio.
Positions which reference a claim on a special purpose entity are not included either.14
An institution may also include in the correlation trading portfolio positions that hedge
the positions described above and which are neither securitization exposures nor n-th-to-
default credit derivatives and where a liquid two-way market as described above exists
for the instrument or its underlyings.
[BCBS December 2010 par 689(iv)]
14 Specifically, a bank must exclude from the correlation trading portfolio any SPV-issued instrument backed,
directly or indirectly, by a position that would itself be excluded if held by the bank directly. Thus, notes issued
by an SPV holding residential or commercial mortgages would not be eligible for inclusion in the correlation
trading portfolio. However, a cash CDO position could be included in the correlation trading portfolio if the
assets underlying the CDO met all of the relevant criteria (eg the underlyings are single-name corporate bonds
having liquid two-way markets).
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86. The specific risk capital charge for the correlation trading portfolio is equal to the
greater of:
a. the total specific risk capital charges that would apply only to the net long positions from
the net long correlation trading exposures combined,
or
b. the total specific risk capital charges that would apply only to the net short positions from
the net short correlation trading exposures combined. The larger of these total amounts is
then the specific risk capital charge for the correlation trading portfolio.15
[BCBS December 2010 par 709(ii)]
Non-correlation trading portfolio products
87. The specific risk capital charge for tranched products that are not eligible for inclusion
in a correlation trading portfolio is calculated by multiplying the absolute values of the tranched
positions in the trading book by their respective charges.
88. For this calculation, offsetting of long and short positions is permitted for tranched
positions in identical issues with identical attachment and detachment points, and underlying
reference names, etc..
89. During a transitional period ending 31 December 2013, the institution may exclude
positions in securitization instruments (and n-th-to-default credit derivatives) which are not
included in the correlation trading portfolio from the above calculation, according to an
equivalent treatment, and determine the specific risk capital charge as follows: The institution
computes (i) the total specific risk capital charge that would apply just to the net long positions
in securitization instruments in the trading book, and (ii) the total specific risk capital charge that
would apply just to the net short positions in securitization instruments in the trading book. The
larger of these total amounts is then the specific risk capital charge for securitization instruments
in the trading book. This calculation must be undertaken separately from the calculation for the
correlation trading portfolio. [BCBS December 2010 par 709(ii-1-)]
90. Institutions using the standardized approach for credit risk must utilize Table III.16 For
positions with long-term ratings of B+ and below and short-term ratings other than A-1/P-1, A-
2/P-2, A-3/P-3, capital 1250% risk weight (100% capital charge), as defined in Chapter 7 –
Structured Credit Products, paragraph 46 is required. A 1250% risk weight (100% capital
charge) is also required for unrated positions with the exception of the circumstances described
in Chapter 7 – Structured Credit Products, section 7.4.3 (iii). The operational requirements for
the recognition of external credit assessments outlined in Chapter 7 – Structured Credit Products,
paragraph 49 apply. [BCBS December 2010 par 712(iv)]
15 Note that the application of the maximum operator to net long positions and net short positions can be done after
considering all permissible netting options (including those considered in section 8.10.1.1). 16 Note that the subsequent paragraph offers alternatives for determining the specific risk capital charge for unrated
exposures for institutions that do not have approval to apply advanced modelling approaches to measure credit
risk in the banking book,
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TABLE III
Specific risk capital charges based on external credit ratings
for institutions using the standardized approach to credit risk
External Credit
Assessment
AAA to AA-
A-1/P-1
A+ to A-
A-2/P-2
BBB+ to
BBB-
A-3/P-3
BB+ to
BB-
Below BB-
and below A-
3/P-3 or
unrated
Securitization
exposures 1.6% 4% 8% 28% 100%
Re-securitization
exposures 3.2% 8% 18% 52% 100%
91. The specific risk capital charges for rated positions covered under the internal ratings-
based approach for securitization exposures are defined in Table IV below. For positions with
long-term ratings of B+ and below and short-term ratings other than A-1/P-1, A-2/P-2, A-3/P-3,
a 1250% risk weight (100% capital charge) as defined in Chapter 7 – Structured Credit Products,
paragraph 45 is required. The operational requirements for the recognition of external credit
c. In all other cases the capital charge can be calculated as 8% of the weighted average risk
weight that would be applied to the securitised exposures under the standardized
approach, multiplied by a concentration ratio. If the concentration ratio is 12.5 or higher
the position receives a 1250% Risk Weight (100% capital charge) as defined in
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Chapter 7 – Structured Credit Products, paragraph 45. This concentration ratio is equal to
the sum of the nominal amounts of all the tranches divided by the sum of the nominal
amounts of the tranches junior to or pari passu with the tranche in which the position is
held including that tranche itself.
93. The resulting specific risk capital charge must not be lower than any specific risk capital
charge applicable to a rated more senior tranche. If an institution is unable to determine the
specific risk capital charge as described above or prefers not to apply the treatment described
above to a position, it must apply a 1250% Risk Weight (100% capital charge) to that position.
[BCBS December 2010 par 712(vi))]
94. A position subject to a 1250% Risk Weight (100% capital charge) according to the
standardized approaches to interest rate specific risk for tranched products may be excluded from
the calculation of the capital charge for general market risk whether the institution applies the
standardized measurement method or the internal models method for the calculation of its
general market risk capital charge. [BCBS December 2010 par 712(vii))]
N-th to default products
95. An n-th-to-default credit derivative is a contract where the payoff is based on the n-th
asset to default in a basket of underlying reference instruments. Once the n-th default occurs the
transaction terminates and is settled.
a. The capital charge for specific risk for a first-to-default credit derivative is the lesser of
(1) the sum of the specific risk capital charges for the individual reference credit
instruments in the basket, and (2) the maximum possible credit event payment under the
contract. Where an institution has a risk position in one of the reference credit
instruments underlying a first-to-default credit derivative and this credit derivative hedges
the institution’s risk position, the institution is allowed to reduce with respect to the
hedged amount both the capital charge for specific risk for the reference credit instrument
and that part of the capital charge for specific risk for the credit derivative that relates to
this particular reference credit instrument. Where an institution has multiple risk positions
in reference credit instruments underlying a first-to-default credit derivative this offset is
allowed only for that underlying reference credit instrument having the lowest specific
risk capital charge.
b. The capital charge for specific risk for an n-th-to-default credit derivative with n greater
than one is the lesser of (1) the sum of the specific risk capital charges for the individual
reference credit instruments in the basket but disregarding the (n-1) obligations with the
lowest specific risk capital charges; and (2) the maximum possible credit event payment
under the contract. For n-th-to-default credit derivatives with n greater than 1 no offset of
the capital charge for specific risk with any underlying reference credit instrument is
allowed.
c. If a first or other n-th-to-default credit derivative is externally rated, then the protection
seller must calculate the specific risk capital charge using the rating of the derivative and
apply the respective securitization risk weights as specified above for tranched products,
as applicable.
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d. The capital charge against each net n-th-to-default credit derivative position applies
irrespective of whether the institution has a long or short position, i.e. obtains or provides
protection.
[BCBS December 2010 par 718]
9.10.1.2 General market risk
Overview
96. An institution may measure its exposure to general market risk using the maturity
method, which uses standardized risk weights that approximate the price sensitivity of various
instruments. The maturity method uses a maturity-ladder that incorporates a series of "time-
bands" that are divided into maturity "zones" for grouping together securities of similar
maturities. These time bands and zones are designed to take into account differences in price
sensitivities and interest rate volatilities across different maturities.
97. A separate maturity ladder must be constructed for each currency in which an institution
has significant positions, and capital requirements must be calculated for each currency
separately. No offsetting of positions is permitted between different currencies in which
positions are significant. Positions in currencies that are not significant may be combined into a
common maturity ladder, with the net long or short position of each currency entered in the
applicable time band. The net positions are to be summed within each time band, irrespective of
whether they are positive or negative, to arrive at the gross position. [BCBS June 2006 par
718(ii)]
98. Opposite positions of the same amount in the same issues (but not different issues by
the same issuer), whether actual or notional, may be excluded from the interest rate maturity
framework, as well as closely matched swaps, forwards, futures, and forward rate agreements
(FRAs) that meet the conditions set out in the sub-section on interest rate derivatives in
Appendix 9-III. [BCBS June 2006 par 718(iii)]
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99. The capital requirement for general market risk, excluding options, is the sum of:
Basis risk charge
Matched weighted positions in all time bands x 10%
Yield curve risk charge
Matched weighted positions in zone 1 x 40%
Matched weighted positions in zone 2 x 30%
Matched weighted positions in zone 3 x 30%
Matched weighted positions between zones 1 and 2 x 40%
Matched weighted positions between zones 2 and 3 x 40%
Matched weighted positions between zones 1 and 3 x 100%
Net position charge
Residual unmatched weighted positions x 100%
100. An example of the calculation of general market risk under the maturity method can be
found in Appendix 9-III.
General market risk calculation
101. To calculate the general market risk charge, the institution distributes the long or short
position (at current market value) of each debt instrument and other source of interest rate
exposure, including derivatives, into the time-bands and three zones of the maturity ladder
outlined in Table V. Once all long and short positions are placed into the appropriate time-
bands, the long positions in each time-band are summed and the short positions in each time-
band are summed.
102. The summed positions are multiplied by the appropriate risk-weight factor (reflecting
the price sensitivity of the positions to changes in interest rates) to determine the risk-weighted
long and short market risk positions for each time-band. [BCBS June 2006 par 718(iv)]
103. The risk weights for each time-band are:
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TABLE V
Maturity Method: Zones, Time-bands and Weights
Zone Time-bands Time-bands Risk Weights
For Coupon 3% or more
For Coupon less than 3%
and zero coupon bonds [%]
1 up to 1 month up to 1 month 0.00
1 up to 3 months 1 up to 3 months 0.20
3 up to 6 months 3 up to 6 months 0.40
6 up to 12 months 6 up to 12 months 0.70
2 1 up to 2 years 1 up to 1.9 years 1.25
2 up to 3 years 1.9 up to 2.8 years 1.75
3 up to 4 years 2.8 up to 3.6 years 2.25
3 4 up to 5 years 3.6 up to 4.3 years 2.75
5 up to 7 years 4.3 up to 5.7 years 3.25
7 up to 10 years 5.7 up to 7.3 years 3.75
10 up to 15 years 7.3 up to 9.3 years 4.50
15 up to 20 years 9.3 up to 10.6 years 5.25
over 20 years 10.6 up to 12 years 6.00
12 up to 20 years 8.00
over 20 years 12.50
104. A capital requirement is calculated for the matched weighted position in each time band
to address basis risk. The capital requirement is 10% of the matched weighted position in each
time band, that is, 10% of the smaller of the risk-weighted long or risk-weighted short position,
or if the positions are equal, 10% of either position.17 If there is only a gross long or only a gross
short position in the time band, a basis risk charge is not calculated. The remainder (i.e., the
excess of the weighted long positions over the weighted short positions, or vice versa, within a
time band) is called the unmatched weighted position for that time band. [BCBS June 2006 par
718(v)]
105. The basis risk charges for each time-band are absolute values, that is, neither long nor
short. The charges for all time-bands in the maturity ladder are summed and included as an
element of the general market risk capital requirement.
106. Capital requirements, referred to as the yield curve risk charge, are assessed to allow for
the imperfect correlation of interest rates along the yield curve. There are two elements to the
yield curve risk charge. The first element is a charge on the matched weighted positions in zones
1, 2 and 3. The second is a capital charge on the matched weighted positions between zones.
17 For example, if the sum of the weighted longs in a time-band is $100 million and the sum of the weighted shorts
is $90 million, the basis risk charge for the time-band is 10% of $90 million, or $9 million.
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107. The matched weighted position in each zone is multiplied by the percentage risk factor
corresponding to the relevant zone. The risk factors for zones 1, 2 and 3 are provided in
Table VI. The matched and unmatched weighted positions for each zone are calculated as
follows. Where a zone has both unmatched weighted long and short positions for various time
bands within a zone, the extent to which the one offsets the other is called the matched weighted
position for that zone. The remainder (i.e., the excess of the weighted long positions over the
weighted short positions, or vice versa, within a zone) is called the unmatched weighted position
for that zone.
108. The matched weighted positions between zones are multiplied by the percentage risk
factor corresponding to the relevant adjacent zones. The risk factors for adjacent offsetting
zones are provided in Table VI. To arrive at the matched weighted positions between zones, the
unmatched weighted positions of a zone may be offset against positions in other zones as
follows.
a. The unmatched weighted long (short) position in zone 1 may offset the unmatched
weighted short (long) position in zone 2. The extent to which unmatched weighted
positions in zones 1 and 2 are offset is described as the matched weighted position
between zones 1 and 2.
b. Then, any residual unmatched weighted long (short) positions in zone 2 may then be
matched by offsetting unmatched weighted short (long) positions between zone 2 and
zone 3.18
c. Then, any residual unmatched weighted long (short) positions in zone 1 may then be
matched by offsetting unmatched weighted long (short) positions in zone 3. The extent to
which the unmatched positions in zones 1 and 3 are offsetting is described as the matched
weighted positions between zones 1 and 3.
109. The yield curve risk charges, like the basis risk charges, are absolute values that are
summed and included as an element of the general market risk capital requirement.
18 For example, if the unmatched weighted position for zone 1 was long $100 and for zone 2 was short ($200), the
capital charge for the matched weighted position between zone 1 and 2 would be 40% of $100, or $40. The
residual unmatched weighted position in zone 2 ($100) also could have been carried over to offset a long position
in zone 3 and would have attracted a 40% charge.
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TABLE VI
Zonal Disallowances
Zone Time-Band Within the
zone
Between
adjacent zones
Between
zones 1-3
1 0-1 month
40%
40%
100%
1-3 months
3-6 months
6-12 months
2 1-2 years
30% 2-3 years
3-4 years
40%
3 4-5 years
30%
5-7 years
7-10 years
10-15 years
15-20 years
over 20 years
110. The net position charge for interest rate position risk in a currency is the absolute value
of the sum of the weighted net open positions in each time band. [BCBS June 2006 par 718(vi)]
Appendix 9-3 - Position Reporting for General Market Risk Calculations
Debt instruments
111. Fixed-rate instruments are allocated according to the remaining term to maturity and
floating-rate instruments according to the next repricing date. A callable bond that has a market
price above par is slotted according to its first call date, while a callable bond with a market price
below par is slotted according to remaining maturity. Mortgage-backed securities are slotted
according to their final maturity dates.
Interest rate derivatives
112. Debt derivatives and other off-balance sheet positions whose values are affected by
changes in interest rates are included in the measurement system described above, except for
options and the associated underlying instrument (the measurement system for options is
described later). A summary of the treatment for debt derivatives is set out in the following
table. [BCBS June 2006 par 718(ix)]
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113. Derivatives are converted into positions in the relevant underlying instrument and are
included in the calculation of specific and general market risk capital charges as described above.
The amount to be included is the market value of the principal amount of the underlying
instrument or of the notional underlying. For instruments where the apparent notional amount
differs from the effective notional amount, an institution must use the effective notional amount.
[BCBS June 2006 par 718(x)]
114. Futures and forward contracts (including FRAs) are broken down into a combination of
a long position and short position in the notional security. The maturity of a future or a FRA is
the period until delivery or exercise of the contract, plus the life of the underlying instrument.19
Where a range of instruments may be delivered to fulfil the contract, the institution may choose
which deliverable instrument goes into the maturity ladder as the notional underlying instrument.
In the case of a future on a corporate bond index, positions are included at the market value of
the notional underlying portfolio of securities. [BCBS June 2006 par 718(xi)]
115. Although an FRA is closely analogous to an interest rate future, the words "buyer" and
"seller" when used in reference to FRAs have the opposite meaning to that used in the financial
futures market. The "buyer" of an FRA is fixing the interest rate on a deposit that it will receive
in the future. Hence, if interest rates rise, the buyer of an FRA receives the difference between
the contracted rate and the new (higher) rate from the seller; that is the buyer makes a gain.
Thus, an institution wishing to hedge against a rise in interest rates may buy an FRA or sell an
interest rate future.
Position Reporting for the Maturity Method
First Reporting Leg Second Reporting Leg
Instrument
Type
Amount Report According to: Amount Report According to:
Interest Rate Swaps:
Pay Fixed - NP Maturity Date + NP Next Settlement Date: Pay
Receive Fixed + NP Maturity Date - NP Next Settlement Date: Receive
Forward Rate Agreements:
Buy (i.e., short) - NP Maturity Date + NP Value Date
Sell (i.e., long) + NP Maturity Date - NP Value Date
3-month BAX Futures:
Buy + NP Maturity Date - NP Maturity Date
+ 3 months
Sell - NP Maturity Date + NP Maturity Date
+ 3 months
19 For example, assuming an April 30 reporting date, a long position in a June three-month bankers acceptance
future (BAX) is recorded as a long position maturing in five months and a short position maturing in two months. NP = Notional principal in relevant currency
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Position Reporting for the Maturity Method
First Reporting Leg Second Reporting Leg
Instrument
Type
Amount Report According to: Amount Report According to:
Gov't Bonds
and Notes
+ NP Maturity Date
Cross Currency Swaps:
Received
Floating
+ NP Value Date +
Frequency**
Pay Floating - NP Value Date +
Frequency**
Receive Fixed + NP Maturity Date
Pay Fixed - NP Maturity Date
FX Forwards + NP
(Buy)
Value Date - NP
(Sell)
Value Date
116. Swaps are treated as two notional positions in the relevant instruments with appropriate
maturities. The receiving side is treated as the long position and the paying side is treated as the
short position.20 The separate sides of cross-currency swaps or forward foreign exchange
transactions are slotted in the relevant maturity ladders for the currencies concerned. For swaps
that pay or receive a fixed or floating interest rate against some other reference price, for
example, an equity index, the interest rate component is slotted into the appropriate repricing
maturity category, with the long or short position attributable to the equity component being
included in the equity framework set out above.21 [BCBS June 2006 par 718(xii)]
117. An institution may offset long and short positions (both actual and notional) in identical
derivative instruments with exactly the same issuer, coupon, currency, and maturity before
slotting these positions into time-bands. A matched position in a future and its corresponding
underlying may also be fully offset and, thus, excluded from the calculation, except when the
future comprises a range of deliverable instruments. However, in cases where, among the range
of deliverable instruments, there is a readily identifiable underlying instrument that is most
** Starting with the value date, move forward in intervals according to the frequency of payments (e.g., 3M, 6M, or
1YR) 20 For example, an interest rate swap under which an institution is receiving floating-rate interest and paying fixed
is treated as a long position in a floating rate instrument with a maturity equivalent to the period until the next
interest reset date and a short position in a fixed-rate instrument with a maturity equivalent to the remaining life
of the swap. 21 An institution with a large swap book may, subject to review by OSFI, use alternative formulae to calculate the
positions to be included in the maturity ladder. For example, an institution could first convert the payments
required by the swap into present values. For that purpose, each payment would be discounted using zero
coupon yields, and the payment's present value entered into the appropriate time-band using procedures that
apply to zero (or low) coupon bonds. The net amounts would then be treated as bonds, and slotted into the
general market risk framework. Such alternative treatments will, however, only be allowed if: (i) OSFI is fully
satisfied with the accuracy of the system being used, (ii) the positions calculated fully reflect the sensitivity of
the cash flows to interest rate changes; and (iii) the positions are denominated in the same currency.
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profitable for the trader with a short position to deliver, positions in the futures contract and the
instrument may be offset. No offsetting is allowed between positions in different currencies.
[BCBS June 2006 par 718(xiii)]
118. Offsetting positions in the same category of instruments can, in certain circumstances,
be regarded as matched and treated by the institution as a single net position that should be
entered into the appropriate time-band. To qualify for this treatment, the positions must be based
on the same underlying instrument, be of the same nominal value, and be denominated in the
same currency. The separate sides of different swaps may also be "matched" subject to the same
conditions. [BCBS June 2006 par 718(xiv)]
119. In addition:
a. For futures, offsetting positions in the notional or underlying instruments to which the
futures contract relates must be for identical instruments and the instruments must mature
within seven days of each other [BCBS June 2006 par 718(xiv)(i)];
b. For swaps and FRAs, the reference rate (for floating rate positions) must be identical and
the coupon closely matched (i.e., within 15 basis points) [BCBS June 2006 par
718(xiv)(ii)]; and
c. For swaps, FRAs and forwards, the next interest reset date, or for fixed coupon positions
or forwards, the remaining maturity must correspond within the following limits: If the
reset (remaining maturity) dates occur within one month, then the reset dates must be on
the same day; if the reset dates occur between one month and one year later, then the
reset dates must occur within seven days of each other, or if the reset dates occur over
one year later, then the reset dates must occur within thirty days of each other
[BCBS June 2006 par 718(xiv)(iii)].
120. Interest rate and currency swaps, FRAs, forward foreign exchange contracts and interest
rate futures are not subject to a specific risk charge. This exemption also applies to futures on a
short-term (e.g., 3-month Bankers Acceptance rate) interest rate index. However, in the case of
futures contracts where the underlying is a debt security, or an index representing a basket of
debt securities, a specific risk charge will apply according to the category of the issuer. [BCBS
June 2006 par 718(xvi)]
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Appendix 9-4 - Sample Steps in the Calculation of General Market Risk for Debt Instruments
using the Maturity Method
121. A hypothetical institution has the following given positions designated as trading:
(a) Qualifying bond, $13.33 million market value, remaining maturity 8 years, coupon 8%.
(b) Government bond, $75 million market value, remaining maturity 2 months, coupon 7%.
(c) Interest rate swap, $150 million, institution receives floating rate interest and pays fixed,
next interest reset after 12 months, remaining life of swap is 8 years (assumes the current
interest rate is identical to the one the swap is based on).
(d) Long position in interest rate future, $50 million, delivery date after 6 months, life of
underlying government security is 3.5 years (assumes the current interest rate is identical
to the one on which the swap is based).
122. The institution would record these instruments as positions in a maturity ladder as
shown below:
Zone
Time-band Position for Instruments: Risk
Weights
Risk
Weighted
Long
Positions
Risk
Weighted
(Short)
positions
in $ millions
A B C D [%]
$ millions $ millions
1
0-1 mth 0.00
1-3 mth $75 0.20 0.15
3-6 mth ($50) 0.40 (0.20)
6-12 mth $150 0.70 1.05
2
1-2 years 1.25
2-3 years 1.75
3-4 years $50 2.25 1.125
3
4-5 years 2.75
5-7 years 3.25
7-10 years $13.33 ($150) 3.75 0.50 (5.625)
10-15 years 4.50
15-20 years 5.25
>20 years 6.00
123. Each position would be multiplied by the risk weight corresponding to the time band in
which it is recorded. The risk-weighted long and risk weighted short positions in each maturity
band are the basis of calculating the general market risk capital charges.
124. The first step in the process of calculating general market risk is to calculate a 10%
basis risk charge on the matched weighted position in each time band. In this example, there are
partially offsetting long and short positions in the 7-10 year time-band, the matched portion of
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which is equal to $500,000 (i.e., 0.50 million). Ten percent of this matched portion is equal to
$50,000 [.10 x 0.50= 0.05 ($50,000)].
In $ millions
Zone Time-band
Risk
Weighted
Long
Positions
Risk
Weighted
(Short)
Positions
Unmatched
Weighted
Position
Step 1
10% Basis risk
charge
1
0-1 mth
1-3 mth 0.15 0.15 n/a
3-6 mth (0.20) (0.20) n/a
6-12 mth 1.05 1.05 n/a
2
1-2 years
2-3 years
3-4 years 1.125 1.125 n/a
3
4-5 years
5-7 years
7-10 years 0.50 (5.625) (5.125) 0.050
10-15 years
15-20 years
>20 years
TOTAL 0.05
125. Step 2 requires the calculation of the yield curve risk charge. The yield curve risk
charge is calculated on the matched weighted position in each zone using the percentage risk
factors in the table below . In this example, a charge would be calculated for zone 1 (step 2(a)).
It would be 40 % of the total offsetting in the zone -- 40% x 0.20 = 0.08 ($80,000). No charge is
required if offsetting does not occur within a zone.
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Zone
Time-band Unmatched
Weighted
Positions
Step 2(a) Step 2(b)
30% to 40% of
Matched weighted
Zone position
40% to 100% Matched
between Zones
1
0-1 mth
1-3 mth 0.15
3-6 mth (0.20)
6-12 mth 1.05
Zone 1 totals long 1.20 0.08 n/a
short (0.20) =.20 x 40% [Zone 1 & 2 net totals are
both long] unmatched 1.00
2
1-2 years
2-3 years
3-4 years 1.125
Zone 2 totals long 1.125 n/a 0.45 = 40% x the lesser of
1.125 and 5.125 Charge on
the offsetting between Zone
2 (long) and Zone 3 (short)]
3
4-5 years
5-7 years
7-10 years (5.125)
10-15 years
15-20 years
>20 years
Zone 3 total short (5.125) n/a 1.0 = 100% x 1.00
[Charge on the offsetting
between Zone 1 and Zone 3]
126. In step 2(b), the yield curve risk charges on matching between residual unmatched
weighted positions in the three zones are calculated. Zone 1 and zone 2 are offset, if possible,
reducing or eliminating the unmatched weighted positions in zone 1 and zone 2, as appropriate.
Zone 2 and zone 3 are then offset, if possible, reducing or eliminating the unmatched weighted
position in zone 2 or zone 3, as appropriate. Zone 3 and zone 1 are then offset, if possible,
reducing or eliminating the unmatched weighted position in zone 3 and zone 1, as appropriate. A
capital requirement is calculated as a percentage of the position eliminated by the inter-zone
offsetting.
127. In the example, a charge would be calculated for adjacent zones 2 and 3 (step 3). It
would be 40 % of the matched weighted positions between the zones -- 40% x 1.125 = 0.45
($450,000). A charge would be calculated between zones 1 and 3 (step 3). It would be 100 % of
the matched positions between the zones -- 100% x 1.00 = 1.00 ($1,000,000).
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128. Step 3 calculates a net position charge equal to the residual unmatched weighted
position. In this example this amounts to $3 million [being the absolute value of the sum of
0.15-.20+1.05+1.125-5.125 = -3.00] and would be included as the net position charge for general
market risk.
129. The total capital requirement for general market risk for this portfolio would be:
1. Basis risk charge
∑ Matched weighted positions in all time bands 50,000
2. Yield curve risk charge
∑ Matched weighted positions in zone 1 80,000
∑ Matched weighted positions in zone 2 n/a
∑ Matched weighted positions in zone 3 n/a
∑ Matched weighted positions between zones 1 and 2 n/a
∑ Matched weighted positions between zones 2 and 3 450,000
∑ Matched weighted positions between zones 1 and 3 1,000,000
3. Net position charge
∑ Residual unmatched weighted positions 3,000,000
TOTAL GENERAL MARKET RISK $4,580,000
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Appendix 9-5 - Summary of Specific and General Market Risk Charges for Interest Rate
Derivatives
[BCBS June 2006 par 718(xviii)]
INSTRUMENT SPECIFIC RISK
CHARGE22
GENERAL MARKET
RISK CHARGE
(Relating to the issuer of the
instrument. There remains a
separate capital requirement for
counterparty credit risk.)
EXCHANGE-TRADED FUTURE
Government security Yes Yes, as two positions
Corporate debt security Yes Yes, as two positions
Index on short-term interest
rates (e.g., Bankers
Acceptances)
No Yes, as two positions
OTC FORWARD
Government security Yes Yes, as two positions
Corporate debt security Yes Yes, as two positions
Index on short-term interest
rates
No Yes, as two positions
FRAs, Swaps No Yes, as two positions
Forward foreign exchange No Yes, as one position in each
currency
Options For each type of transaction,
either:
Government security Yes Carve out together with the
associated hedging positions
- simplified approach
- scenario analysis
- internal models
Corporate debt security Yes Same as above
Index on short-term interest
rates
No Same as above
22 Refer to Table I in section 9.10.1.1.
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General market risk – credit derivatives
130. General market risk for credit derivatives is calculated using the same methodology as
that used for cash market debt instruments as described in this guideline. As a result, the
combinations for general market risk charges are more limited than those combinations relating
to specific risk.
131. Most credit default products do not create a general market risk position for either the
guarantor or the beneficiary, since they are written against one counterparty's potential default.
There is no risk exposure to market movements.
132. Total rate of return products create a long or short position in the reference asset as well
as a short or long position in the notional bond representing the interest rate related leg of the
contract. These positions should be incorporated into a maturity ladder using standardized risk
weights that approximate the price sensitivity of the instruments. Long or short positions in
reference assets that are created on account of total rate of return products are eligible for netting
using the same treatment as for other asset positions in the maturity ladder calculation.
133. Credit-linked note products create a long position in the note itself but the position is
only applied to the note purchaser (i.e., the guarantor).
9.10.2. Equities risk
134. This section sets out the minimum capital associated with an institution's risk of holding
or taking positions in equities within the trading book. An institution which holds equity
positions (whether long or short) in the trading book is exposed to the risk that the value of
individual equity positions relative to the market may move against the institution - specific risk-
and that the equity market as a whole may move against it - general risk. The specific risk
requirements recognize that individual equities are subject to issuer risk and liquidity risk, and
that these risks may be reduced by portfolio diversification. The general risk requirements set
out in this section recognize offsetting positions within national markets. A separate subsection
for equity derivatives positions outlines the method for including them in the capital calculation.
135. Equity risk capital requirements will apply to positions and exposures in the trading
book on the following instruments:
a. common shares,
b. convertible preference shares or securities,
c. convertible debt securities which convert into equity instruments and are trading as
equities23,
d. depository receipts,
e. any other instruments exhibiting equity characteristics, and
23 See section 9.10.1. for the definition of when a convertible security is trading like an equity.
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f. equity derivatives or derivatives based on above securities.
Non-convertible preference shares are to be excluded from these calculations, as they are
covered by the interest rate risk requirements described in section 9.10.1. [BCBS June 2006
par 718(xix)]
136. Equity positions should be allocated to the country in which each equity is listed and the
calculations outlined below applied to each country. Equity securities listed in more than one
country must be allocated to either (i) the country where the issuer is incorporated and listed or,
(ii) the country where the security was purchased or sold, but not both. Switching between
countries is not permitted and any foreign exchange position resulting from a long or short
position in an equity listed in a country other than Canada must be included in the calculation of
the foreign exchange risk capital requirement. Conversion into the institution's reporting
currency should be done at current spot foreign exchange rates. Matched positions in each
identical equity or stock index in each country may be fully offset, resulting in a single net short
or long position to which the specific and general market risk charges will apply. [BCBS June
2006 par 718(xxiv)]
9.10.2.1. Specific risk
137. The measurement of specific risk capital requirements is calculated on the basis of the
institution's gross equity positions. The gross position is the sum of the absolute value of all
short equity positions and all long equity positions, including positions arising from derivatives,
calculated at the current market value. Long and short positions in the same share issue may be
reported on a net basis. [BCBS June 2006 par 718(xx)]
138. The specific risk capital requirement for equity positions is 8% of this sum. [BCBS
December 2010 par 718 (xxi)]
9.10.2.2. General market risk
139. To calculate general market risk, long and short positions in equity instruments are
offset to arrive at a net position. Instruments are valued at current market and a net position must
be separately calculated for each country in which the institution holds equity instruments. The
capital requirement for general market risk is 8% of the net position for each country. [BCBS
June 2006 par 718 (xxi)]
9.10.2.3. Equity derivatives
140. Equity derivatives and other off-balance sheet positions that are affected by changes in
equity prices are included in the measurement system (except for equity options, equity index
options, and the associated underlying).24 This includes futures and swaps on both individual
24 Where equities are part of a forward contract (both equities to be received or to be delivered), any interest rate or
foreign currency exposure from the other side of the contract should be included in the measurement systems in
sections 9.10.1 or 9.10.2, as appropriate.
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equities and on equity indices. Equity derivatives should be converted into notional equity
positions in the relevant underlying instrument. A summary of the rules for equity derivatives is
set out in Appendix 9-VI. [BCBS June 2006 par 718(xxi)]
Calculation of positions
141. In order to calculate the specific and general market risk, positions in derivatives should
be converted into notional equity positions as follows:
a. futures and forward contracts relating to individual equities should be reported at current
market price of the underlying;
b. futures relating to stock indices should be reported as the marked-to-market value of the
notional underlying equity portfolio;
c. equity swaps are to be treated as two notional positions; and
d. equity options should be carved out together with the associated underlyings and treated
under section 9.10.5. [BCBS June 2006 par 718(xxiii)]
Risk in relation to an index
142. A specific risk capital charge of 2% applies to the net long or short position in a contract
on an index listed in Table I below. This capital charge is intended to cover factors such as
divergence from the general market level and execution risk. The 2% risk weight is to apply
only to well diversified indices and not, for example, to sectoral indices. [BCBS June 2006 par
718(xxv)]
143. Positions in indices not listed in Table I must either be decomposed into their
component shares, or be treated as a single position based on the sum of current market values of
the underlying instruments; if treated as a single position, the specific risk requirement is the
highest specific risk charge that would apply to any of the index's constituent shares. An
institution's position in an index contract is also subject to an 8% general market risk charge.
TABLE I
MARKET INDICES
Australia S&P/ASX 200 Netherlands EOE 25
Austria ATX Spain IBEX 35
Belgium BEL 20 Sweden OMX
Canada S&P/TSX 60 Switzerland SMI
France CAC 40 United Kingdom FTSE 100
Germany DAX United Kingdom FTSE mid-250
Japan Nikkei 25 United States S&P 500
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Futures arbitrage
144. In the case of futures-related arbitrage strategies, the 2% specific risk charge described
above may be applied to only one index with the opposite position exempt from a capital charge
(both the specific and general market risk capital charges). The strategies qualifying for this
treatment are:
a. when the institution takes an opposite position in exactly the same index future at
different dates; and
b. when the institution has an opposite position in different but similar indices at the same
date, subject to supervisory oversight. [BCBS June 2006 par 718(xxvi)]
145. If an institution engages in a deliberate arbitrage strategy, in which a futures contract on
a well-diversified25 equity index matches a basket of securities, it may exclude both positions
from their respective specific and general risk charges on condition that the trade has been
deliberately entered into and separately controlled and the composition of the basket of stocks
represents at least 90% of the market value of the index.
146. In such a case, there will be a minimum capital requirement of 4% (that is, 2% of the
gross value of the positions on each side) to reflect risk associated with executing the transaction.
This applies even if all of the securities comprising the index are held in identical proportions.
Any excess value of the securities comprising the basket over the value of the futures contract or
excess value of the futures contract over the value of the basket is treated as an open long or
short position. [BCBS June 2006 par 718(xxvii)]
25 A portfolio that is well-diversified is characterized by a limited sensitivity to price changes of any single equity
issue or closely related group of equity issues held in the portfolio. The volatility of the portfolio's value should
not be dominated by the volatility of any individual equity issue or by equity issues from any single industry or
economic sector.
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Appendix 9-6 - Summary of Treatment for Equity Derivatives
[BCBS June 2006 par 718(xxix)]
INSTRUMENT SPECIFIC RISK GENERAL MARKET RISK
(relating to the issuer of the
instrument. There remains a
separate capital requirement for
counterparty credit risk)
Futures, Swaps, & Similar
OTC Contracts
Individual equity Yes Yes, as underlying
Index 2.0% Yes, as underlying
Options
Individual equity Yes Carve out from equity position risk
framework together with the
associated hedging positions and
apply:
simplified approach; or
scenario approach; or
internal models.
Index 2.0%
9.10.3. Foreign exchange position risk
147. This section sets out a shorthand method for calculating the minimum capital required
to cover the risk of holding or taking a position in foreign currencies including gold. [BCBS June
2006 par 718(xxx)]
148. Institutions with significant foreign exchange positions are encouraged to use internal
models.
149. The capital requirement for foreign exchange risk is applied to the entire business, both
the trading and non-trading books. Two steps are required to calculate the capital requirement
for foreign exchange risk. The first is to measure the exposure in a single currency position. The
second is to calculate the capital requirement for the portfolio of positions in different currencies.
[BCBS June 2006 par 718(xxxi)]
150. In summary, the capital charge is 8% of the greater of the sum of (i) the net open long
positions or (ii) the net open short positions in each currency, plus the net open position in gold,
whatever the sign.26 [BCBS June 2006 par 718(xli)]
26 Gold is treated as a foreign exchange position rather than a commodity because its volatility is more in line with
foreign currencies and institutions manage it in a manner similar to foreign currencies.
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9.10.3.1. Measuring the exposure in a single currency
151. The net open position for each individual currency (and gold) is calculated by summing:
a. the net spot position (i.e., all asset items less all liability items, including accrued interest
and accrued expenses, denominated in the currency in question),
b. the net forward position (i.e., all net amounts under forward foreign exchange
transactions, including currency futures and the principal on currency swaps),
c. guarantees (and similar instruments) that are certain to be called and are likely to be
irrecoverable,
d. net future income/expenses not yet accrued but already fully hedged (at the discretion of
the reporting institution), and
e. any other item representing a profit or loss in foreign currencies. [BCBS June 2006 par
718(xxxii)]
Options on foreign exchange are treated separately; see section 9.10.5.
Treatment of immaterial operations
152. Foreign exchange risk is assessed on a consolidated basis. It may be technically
impractical in the case of immaterial operations to include some currency positions. In such
cases, the internal limit in each currency may be used as a proxy for the positions, provided there
is adequate ex post monitoring of actual positions complying with such limits. In these
circumstances, the limits should be added, regardless of sign, to the net open position in each
currency. [BCBS June 2006 par 718(xli), footnote 139]
Measurement of forward currency positions
153. Forward currency positions should be valued at current spot market exchange rates. It
would be inappropriate to use forward exchange rates since, to some extent they reflect current
interest rate differentials. Institutions that base their normal management accounting on net
present values are expected to use the net present values of each position, discounted using
current interest rates and translated at current spot rates, for measuring their forward currency
and gold positions. [BCBS June 2006 par 718(xxxvi)]
Accrued and unearned interest, income and expenses
154. Accrued interest, accrued income and accrued expenses should be treated as a position
if they are subject to exchange rate fluctuations. Unearned but expected future interest, income
or expenses may be included, provided the amounts are certain and have been fully hedged by
forward foreign exchange contracts. Institutions must be consistent in their treatment of
unearned interest, income and expenses and must have written policies covering the treatment.
The selection of positions that are only beneficial to reducing the overall position will not be
permitted. [BCBS June 2006 par 718(xxxv)]
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Structural positions
155. Structural positions and related hedges will be exempt from the calculation of net open
currency positions. Structural positions may include any of the following:
a. any position arising from an instrument that qualifies to be included in an institution's
capital base,
b. any position entered into in relation to the net investment of a capital nature in foreign
operation, the accounting consequence of which is to reduce or eliminate what would
otherwise be a movement in the foreign currency translation reserved, and
c. investments in foreign operations that are fully deducted from an institution's capital for
capital adequacy purposes. [BCBS June 2006 par 718(xxxviii)]
9.10.3.2. Calculating the capital requirement for the portfolio
156. The nominal amount (or net present value) of the net open position in each foreign
currency (and gold) is converted at spot rates into Canadian dollars. The capital charge is 8% of
the overall net open position calculated as the sum of:
a. the greater of the sum of the net open short positions or the sum of the net open long
positions (absolute values), and
b. the net open position in gold, either long or short, regardless of sign.[BCBS June 2006
par 718(xli)]
9.10.3.3. Foreign exchange de minimus criteria
157. An institution doing negligible business in foreign currency, and that does not take
foreign exchange positions for its own account, may be exempted from the capital requirement
for foreign exchange risk provided that:
a. Its foreign currency business, defined as the greater of the sum of its gross long positions
and the sum of its gross short positions in all foreign currencies, does not exceed 100% of
eligible capital, and
b. Its overall net open foreign exchange position does not exceed 2% of its eligible capital.
[BCBS June 2006 par 718(xlii)]
Appendix 9-7 - Example of the Shorthand Measure of Foreign Exchange Risk
158. Institution A has the following net currency positions. These open positions have been
converted at spot rates to the reporting currency, in this case Canadian dollars, (+) signifies a
long position and (-) signifies a short position.
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Table I
YEN Euro GB£ CHF US$ GOLD
+50 +100 +150 -20 -180 -35
+300 -200 -35
159. In this example, the institution has three currencies in which it has long positions, these
being the Japanese Yen, the Euro and the British Pound, and two currencies in which it has a
short position, the Swiss Franc and the U.S. Dollar. The middle line of the above chart shows
the net open positions in each of the currencies. The sum of the long positions is +300. The sum
of the short positions is -200.
160. The foreign exchange market risk is calculated using the higher of the summed absolute
values of either the net long or short positions, and the absolute value for the position in gold.
The capital charge is 8%. In this example, the total long position (300) would be added to the
gold position (35) to give an aggregate position of 335. The aggregated amount multiplied by
8% would result in a capital charge of $26.80.
9.10.4. Commodities risk
161. This section provides a minimum capital requirement to cover the market risk of
holding or taking positions in commodities, including precious metals but excluding gold (gold is
treated as a foreign currency). Institutions conducting a limited amount of commodities business
may use the simplified measurement method that is comprised of a capital charge on the net and
gross position in each category of commodity. This method is set out below. All other
institutions must adopt an internal model system that conforms to criteria set out in section 9.11.
Net position requirement
162. Under the simplified method, each long and short commodity position (spot and
forward) is expressed in terms of the standard unit of measurement (such as barrels, kilos, or
grams). The open positions in each category27 of commodities are then converted at current spot
rates into Canadian dollars, with long and short positions offset to arrive at the net open position
in each commodity. [BCBS June 2006 par 718(xlix)]
163. Positions in different categories of commodities may not be offset. The base capital
requirement is 15% of the net open position, long or short, in each commodity.28 [BCBS June
2006 par 718(liv)]
27 Commodities that are deliverable against each other or that are close substitutes with a minimum correlation of
ninety percent between price movements are considered to be part of the same category. 28 When the funding of a commodity position opens an institution to interest rate or foreign exchange exposure, the
relevant positions should be included in the measures of interest rate and foreign exchange risk described in
sections 9.10.1. and 9.10.2. When a commodity is part of a forward contract, any interest or foreign currency
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Gross position requirement
164. To protect an institution against basis risk, interest rate risk, and forward gap risk, each
category of commodity is also subject to a 3% capital requirement on the institution's gross
positions, long plus short, in the particular commodity. [BCBS June 2006 par 718(lv)]
Calculation of positions
165. Commodity derivatives and other off-balance-sheet positions that are affected by
changes in commodity prices are included in the measurement system (except for options and the
associated underlying instrument - refer to section 9.10.5 and Appendix 9-VIII for a description
of their treatment). Commodity derivatives are converted into notional commodity positions
using the current spot price. [BCBS June 2006 par 718(liii)]
9.10.5. Options
166. Options contracts and related hedging positions in the associated underlying instrument,
commodity or index, cash or forward, are subject to capital requirements as calculated in this
section. The capital requirements calculated under this section should then be added to the
capital requirements for debt securities, equities, foreign exchange, and commodities risk as
appropriate. Two alternatives to measuring the market risk for options activities are available
under the standardized approach:
a. institutions which solely use purchased options may use the simplified method
b. institutions which also write options must use the scenario method29
167. The more significant an institution's trading in options, the more sophisticated the
approach an institution will be expected to use. Institutions doing business in certain classes of
exotic options (e.g., barriers and digitals) may be required to use the internal models alternative
as set out in section 9.11. [BCBS June 2006 par 718(lvi)]
168. Regardless of the method used, specific risk related to the issuer of an instrument still
applies to options positions for equities, equity indices and corporate debt securities.
In addition to these market risk charges, purchased options remain subject to the credit risk
capital requirements specified in Chapter 3 – Credit Risk – Standardized Approach.
9.10.5.1. Simplified method
169. An institution that has only a limited amount and range of purchased options may use
the simplified method set out in Table I for individual options positions. These options positions
exposure from the other side of the contract should be appropriately included in the measurement systems in
sections 9.10.1. and 9.10.2. 29 Unless all their written option positions are hedged by perfectly matched long positions in exactly the same
options, in which case there is no capital requirement for market risk.
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are subject to the separate capital charges specified in Table I and are not included in the
standardized calculation of specific and general market risk specified in the preceding sections.
A charge must be calculated for each individual option in which the institution has a position.
170. As an example of how the calculation in Table I would work, if a holder of 100 shares
currently valued at $10 each has an equivalent put option with a strike price of $11, the capital
charge would be: $1,000 x 16.0% (e.g., 8.0% specific plus 8.0% general market risk) = $160,
less the amount the option is in the money ($11 - $10) x 100 = $100, i.e., the capital charge
would be $60. A similar methodology applies for options whose underlying is a foreign
currency, a debt security or a commodity. However, in the case of options on foreign exchange
and options on commodities, only the risk factor for general market risk will be applied to the
relevant options position. [BCBS June 2006 par 718(lviii)]
Table I
Simplified Method: Capital Charges
Position Treatment
Long the underlying and Long
the put
The capital charge will be the market value of the underlying
instrument30 multiplied by the sum of specific and general market risk
charges31 specified in the preceding sections for the underlying less
the amount the option is in the money (if any) bounded at zero32 Or
Short the underlying and Long
the call
Long call The capital charge will be the lesser of:
Or (i) the market value of the underlying instrument multiplied by the
sum of specific and general market risk charges (refer to
footnote 29) for the underlying Long put
(ii) the market value of the option33
30 In some cases such as foreign exchange, it may be unclear which side is the ''underlying instrument''; this should
be taken to be the asset that would be received if the option were exercised. In addition the nominal value
should be used for items where the market value of the underlying instrument could be zero, e.g., caps and floors
and swaptions, etc. 31 To determine the appropriate specific risk and general market risk factors, refer to the preceding sections on
interest rate positions risk, equity risk, foreign exchange risk and commodity risk. Some options (e.g., where the
underlying is an interest rate, a currency or a commodity) bear no specific risk but specific risk will be present in
the case of options on certain interest rate related instruments (e.g., options on a corporate debt security or
corporate bond index) and for options on equities and stock indices (see the section on equity position risk).
Accordingly, the combined charge under this measure for currency options will be 8% and for options on
commodities, 15% (the additional 3% charge is not added because options are not netted). 32 For options with a residual maturity of more than six months, the strike price should be compared with the
forward, not current, price. An institution unable to do this must take the in the money amount to be zero. 33 Where the position does not fall within the trading book (i.e., options on certain foreign exchange or
commodities positions not belonging to the trading book), it may be acceptable to use the book value instead.
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9.10.5.2. Scenario method
171. Under the scenario method, an institution is required to make separate calculations of
the specific risk and general market risk of options and their related hedging positions. Specific
risk charges must be calculated on each issue in which the institution has a net option position
that is subject to interest rate risk or to equity risk. General risk charges are calculated on
portfolios of options (groupings are set out below).
172. The scenario method uses simulation techniques to calculate changes in the value of an
options portfolio for changes in the level and volatility of the prices of its associated underlying
instruments. Under this approach, the general market risk charge is determined by the scenario
"matrix" (i.e., the specified combination of underlying and volatility changes) that produces the
largest loss. The total general market risk capital requirement for all option portfolios is the sum
of the largest losses of individual option portfolios. [BCBS June 2006 par 718(lxiii)]
173. In addition to the general market risk of its interest rate and equity options portfolios,
institutions using the scenario method are required to calculate the specific risk of these options
using the same basic methodology in the preceding sections on interest rate position risk and
equity risk.
Calculating the general market risk
174. An institution constructs a two-dimensional matrix for each of its options portfolios.
Options portfolios include options and any related hedging positions grouped together as
follows:
a. for interest rates, options on underlying instruments whose residual maturity is bounded
by one of at least six groups of time bands from Table II of this section where no more
than three contiguous time bands are grouped together [BCBS June 2006 par 718(lxiii)],
b. for equities and equity indices, each national market,
c. for foreign currencies and gold, each currency pair and gold, and
d. for commodities, each individual commodity.
175. The first dimension of each matrix requires the institution to evaluate the portfolio over
a specified range above and below the current value of the underlying instrument, commodity, or
index.
176. For interest rates the range is consistent with the assumed changes in yield for the time
bands in Table II. Institutions should use the highest of the assumed changes in yield applicable
to the time bands that it groups together. The time bands and assumed changes in yield are:
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Table II
Time band Assumed changes
in yield
Time band Assumed changes
in yield
up to 1 month 1.00 3 up to 4 years 0.75
1 up to 3 months 1.00 4 up to 5 years 0.75
3 up to 6 months 1.00 5 up to 7 years 0.70
6 up to 12 months 1.00 7 up to 10 years 0.65
1 up to 2 years 0.90 10 up to 15 years 0.60
2 up to 3 years 0.80 15 up to 20 years 0.60
over 20 years 0.60
177. The other ranges are ±8% for equities, ±8% for foreign exchange and gold, and ±15%
for commodities.
178. For all option portfolios, at least seven observations (including the current observation)
should be used to divide the range into equally spaced intervals. [BCBS June 2006 par 718(lxiv)]
179. The second dimension of the matrix entails a change in the volatility of the underlying
rate or price equal to ± 25% of the current volatility.34 [BCBS June 2006 par 718(lxv)]
180. The application of the scenario method, particularly regarding the precise way the
analysis is constructed, will be subject to review by OSFI. An institution using the scenario
method should meet the appropriate qualitative standards set forth in the section on the internal
models approach. [BCBS June 2006 par 718(lxvii)]
Calculating the specific risk of options on debt and equity securities
181. The specific risk charge for options on debt securities is calculated by multiplying the
market value of the effective notional amount of the debt instrument that underlies an option by:
the option's delta; and
by the specific risk factors in Table I of section 9.10.1.1 that correspond to the category
and residual term of the underlying debt instrument.
34 For example, if the underlying of an equity instrument has a current market value of $100 and a volatility of
20%, the first dimension of the grid would range from $92 to $108, divided into eight intervals of $2.00 and the
second dimension would assume volatility stays at 20%, increases to 25% (20% + (.20 x .25)) and decreases to
15% (20% - (.20 x .25)).
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182. The specific risk charge for options on equity securities and options on an equity index
is calculated by multiplying the market value of the effective notional amount of the equity
instrument or equity index that underlies an option by:
the option's delta; and
then by:
8%, or
2% if the option is based on an index of equities.
183. The effective notional amount of an option is the market value of the stated underlying
debt or equity instrument or equity index adjusted to reflect any multiplier applicable to the
contract's reference rate(s) or, where there is no multiplier component, simply, the market value
of the stated underlying debt or equity instrument or the notional amount underlying an option on
an equity index. [BCBS June 2006 par 718(lvii)]
Appendix 9-8 - Example of Options Scenario Matrices
184. A hypothetical institution has purchased and sold options on Canadian interest rates,
and options to purchase and sell U.S. dollars with Canadian funds. The institution might use the
scenario approach to calculate the general market risk of these options portfolios by calculating
including related options volatilities in each risk factor category). OSFI may also
recognize empirical correlations across broad risk factor categories, provided OSFI is
satisfied that the institution's system for measuring correlations is sound and implemented
with integrity. [BCBS June 2006 par 718(lxxvi)(g)]
h. Institutions’ models must accurately capture the unique risks associated with options
within each of the broad risk categories. The following criteria apply to the measurement
of options risks:
Institutions’ models must capture the non-linear price characteristics of options
positions;
Institutions are expected to ultimately move towards the application of a full 10-
day price shock to options positions or positions that display option-like
characteristics. In the interim, OSFI will accept estimates of less than a 10 day
price shock that are adjusted to an equivalent 10 day price shock using a square
root of time adjustment; and
Each institution's risk measurement system must have a set of risk factors that
captures the volatilities of the rates and prices underlying option positions, i.e.,
vega risk. Institutions with relatively large and/or complex options portfolios
should have detailed specifications of the relevant volatilities. This means that
institutions should measure the volatilities of the options positions broken down
by different maturities. [BCBS June 2006 par 718(lxxvi)(h)]
i. In addition, an institution must calculate a ‘stressed value-at-risk’ measure. This measure
is intended to replicate a value-at-risk calculation that would be generated on the
institution’s current portfolio if the relevant market forces experienced a period of stress;
and should therefore be based on the 10-day, 99th percentile, one-tailed confidence
interval value-at-risk measure of the current portfolio, with model inputs calibrated to
historical data from a continuous 12-month period of significant financial stress relevant
to the institution’s portfolio. The period used must be approved by the OSFI and
regularly reviewed. As an example, for many portfolios, a 12-month period relating to
significant losses in 2007/08 would adequately reflect a period of such stress; although
other periods relevant to the current portfolio must be considered by the institution.
[BCBS December 2010 par 718(lxxvi)(i)]
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198.i. OSFI Notes
In a selection among candidate 12-month stress periods, banks must maintain
sufficient observational data to always re-consider prior selection choices. In doing
so no observational data is dropped due to passage of time.
j. As no particular model is prescribed for measuring value-at-risk above, different
techniques might need to be used to translate the current model used for value-at-risk into
one that delivers a stressed value-at-risk. For example, institutions should consider
applying anti-thetic37 data, or applying absolute rather than relative volatilities to deliver
an appropriate stressed value-at-risk. The stressed value-at-risk should be calculated at
least weekly. [BCBS December 2010 par 718(lxxvi)(j)]
k. Each institution must meet, on a daily basis, a capital requirement expressed as the sum
of:
The higher of (1) the previous day's value-at-risk number measured according to
the parameters specified in this section (VaRt−1); and (2) an average of the daily
value-at-risk measures on each of the preceding sixty business days (VaRavg),
multiplied by a multiplication factor (mc);
Plus
The higher of (1) its latest available stressed-value-at-risk number (sVaRt−1); and
(2) an average of the stressed value-at-risk numbers over the preceding sixty
business days (sVaRavg), multiplied by a multiplication factor (𝑚𝑠).
Therefore, the capital requirement (c) is calculated according to the following
formula:
c = max{VaRt−1; mc ∙ VaRavg} + max{sVaRt−1; ms ∙ sVaRavg}
[BCBS December 2010 par 718(lxxvi)(k)]
l. The multiplication factors mc and ms will be set by OSFI on the basis of its assessment of
the quality of the institution’s risk management system, subject to an absolute minimum
of 3. Institutions will be required to add to these factors a “plus” directly related to the ex-
post performance of the model, thereby introducing a built-in positive incentive to
maintain the predictive quality of the model. The plus factors can exceed 1 depending on
the outcome of so-called “backtesting.” The backtesting results applicable for calculating
the plus factors are based on value-at-risk only and not stressed value-at-risk. If the
backtesting results are satisfactory and the institution meets all of the qualitative
standards set out below in section 9.11.5 the plus factors could be zero. Institutions must
37 Institutions should consider modelling valuation changes that are based on the magnitude of historic price
movements, applied in both directions – irrespective of the direction of the historic movement. For example, if a
time series included a significant upward spike in equity prices, the model could apply significant movements in
equity prices both upwards and downwards. This might be particularly relevant if a bank’s portfolio is the “right
way” to a period of financial stress (ie is long equities in a period of stock market surge); the model used should
reflect that open risk positions (in either direction) are vulnerable to stressed variables.
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perform backtesting on hypothetical outcomes (i.e. using changes in the portfolio value
that would occur were end-of-day positions to remain unchanged). [BCBS December
2010 par 718(lxxvi)(l)]
198.l. OSFI Notes
Stressed VaR multipliers will never be lower than VaR multipliers.
Plus factors will only exceed 1 when a model modification has resulted in a material
change in measured capital requirements.
m. Institutions using models will also be subject to a separate capital charge to cover the
specific risk of interest rate related instruments and equity securities38, as defined sections
9.10.1. and 9.10.2., to the extent that this risk is not incorporated into their models. The
options for calculating the specific risk capital charge are set out in section 9.11.5.
[BCBS June 2006 par 718(lxxvi)(k), revised December 2010 par 718(lxxvi)(m)]
9.11.5. Specific risk calculation
199. Institutions using an internal VaR model may calculate their specific risk capital charge
for equity risk positions using modelled estimates if they meet all of the qualitative and
quantitative requirements for general risk models as well as the additional criteria and
requirements set out in sections 9.11.5.1 (criteria) and 9.11.6 (backtesting) below. Such
institutions are not required to subject their equity positions to the capital charge according to the
standardized measurement method as specified section 9.10.2. [BCBS December 2010 par
718(lxxxvii)]
200. For interest rate risk positions other than securitization exposures and n-th-to-default
credit derivatives, an institution will not be required to subject these positions to the standardized
capital charge for specific risk, as specified in non-tranched sub-sections of 9.10.1.1, when all of
the following conditions hold: [BCBS December 2010 par 718(lxxxvii-1-)]
a. The institution has a value-at-risk measure that incorporates specific risk and meets all
the qualitative and quantitative requirements for general market risk models, as well as
the additional criteria and requirements set out in sections 9.11.5.1 (criteria) and 9.11.6
(backtesting); [BCBS December 2010 par 718(lxxxvii-1-)(a)],
and
b. OSFI is satisfied that the institution’s internally developed approach adequately captures
incremental default and migration risks for positions subject to specific interest rate risk
according to the standards laid out in Appendix 9-IX below. [BCBS December 2010 par
718(lxxxvii-1-)(b)]
38 Including the additional requirements set out in section 9.10.2 for equity indices.
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201. In the criteria below, event risk is defined as the risk of loss in the value of claims
against a borrower or security issuer when that issuer experiences an event other than default or
rating migration which so greatly modifies net worth or future earnings prospects of the issuer
that the market value of the securities is sharply affected. Default risk is narrowly defined as the
risk of loss in the value of claims against a borrower or security issuer when that borrower has
insufficient assets to meet its obligations or is otherwise prevented from meeting its obligations
in a timely manner.
OSFI Notes
202. Banks with permission to use value-at-risk measures for specific risk must also
incorporate a stressed value-at-risk measure into their capital requirements.
203. The institution is allowed to include its securitization exposures and n-th-to-default
credit derivatives in its value-at-risk measure. Notwithstanding, it is still required to hold
additional capital for these products according to the standardized measurement methodology,
with the exceptions noted section 9.11.5.2 under the comprehensive risk measure below. [BCBS
December 2010 par 718(lxxxvii-1-)]
9.11.5.1 Criteria
204. Modelled estimates of specific risk must capture all material components of price risk39
and be responsive to changes in market conditions and compositions of portfolios. In particular,
the model must:
a. explain the historical price variation in the portfolio40,
b. demonstrably capture concentrations (magnitude and changes in composition)41,
c. signal rising risk in an adverse environment42,
d. capture name-related basis risk43,
39 Institutions need not capture default and migration risks for positions subject to the incremental risk capital
charge referred to in Appendix 9-IX. 40 The key ex ante measures of model quality are "goodness-of-fit" measures that address the question of how much
of the historical variation in price value is explained by the risk factors included within the model. One measure
of this type that can often be used is an R-squared measure from regression methodology. If this measure is to be
used, the risk factors included in an institution’s model would be expected to be able to explain a high
percentage, such as 90%, of the historical price variation or the model should explicitly include estimates of the
residual variability not captured in the factors included in this regression. For some types of models, it may not
be feasible to calculate a goodness-of-fit measure. In such instances, an institution will be expected to work with
OSFI to define an acceptable alternative measure that meets this regulatory objective. 41 The institution would be expected to demonstrate that the model is sensitive to changes in portfolio construction
and that higher capital charges are estimated for portfolios that have increasing concentrations in particular
names or sectors. 42 This could be achieved by incorporating in the historical estimation period of the model at least one full credit
cycle and ensuring that the model would not have been inaccurate in the downward portion of the cycle. Another
approach for demonstrating this is through simulation of historical or plausible worst-case environments.
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e. capture event risk44, and
f. be validated through backtesting aimed at assessing whether specific risk, as well as
general market risk, is being adequately captured.
[BCBS December 2010 par 718(lxxxviii)]
205. As techniques and best practices evolve, institutions should incorporate these advances
into their models. [BCBS June 2006 par 718(xci)]
206. The institution’s model must conservatively assess the risk arising from less liquid
positions and/or positions with limited price transparency under realistic market scenarios. In
addition, the model must meet minimum data standards. Proxies may be used only where
available data is insufficient or is not reflective of the true volatility of a position or portfolio,
and only where they are appropriately conservative. [BCBS June 2006 par 718(xc)]
OSFI Notes
207. Banks should include all sovereign debt in their interest rate specific risk value-at-risk
models. Exclusions are permitted to the extent that they represent obligations issued in the
domestic currency and would already be captured in the construction of a benchmark general
market interest rate curve.
208. An institution must have an approach in place to capture in its regulatory capital default
and migration risks in positions subject to a capital charge for specific interest rate risk, with the
exception of securitization exposures and n-th-to-default credit derivatives, that are incremental
to the risks captured by the VaR-based modeled estimate for specific risk (“incremental risks”).
No specific approach for capturing the incremental risks is prescribed Appendix 9-IX presents
guidelines around positions and risks that are covered by this incremental risk capital charge.
[BCBS December 2010 par 718(xcii)]
209. The institution must demonstrate that the approach used to capture incremental risks
meets a soundness standard comparable to that of the internal-ratings based approach for credit
risk as set forth in this guideline, under the assumption of a constant level of risk, and adjusted
where appropriate to reflect the impact of liquidity, concentrations, hedging and optionality. An
institution that does not capture incremental risks through an internally developed approach must
use the specific risk capital charges under the standardized measurement method as set out in
section 9.10.1.1. [BCBS December 2010 par 718(xciii)]
43 Institutions should be able to demonstrate that the model is sensitive to material idiosyncratic differences
between similar but not identical positions, for example debt positions with different levels of subordination,
maturity mismatches, or credit derivatives with different default events. 44 For debt positions, this should include migration risk. For equity positions, events that are reflected in large
changes or jumps in prices must be captured, e.g. merger break-ups/takeovers. In particular, firms must consider
issues related to survivorship bias.
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9.11.5.2 Comprehensive risk measure
210. Subject to OSFI approval, an institution may incorporate its correlation trading portfolio
in an internally developed approach that adequately captures not only incremental default and
migration risks, but all price risks (“comprehensive risk measure”). The value of such products is
subject in particular to the following risks that must be adequately captured:
the cumulative risk arising from multiple defaults, including the ordering of defaults, in
tranched products;
credit spread risk, including the gamma and cross-gamma effects;
volatility of implied correlations, including the cross effect between spread and
correlations;
basis risk, including both
o the basis between the spread of an index and those of its constituent single names; and
o the basis between the implied correlation of an index and that of bespoke portfolios;
recovery rate volatility, as it relates to the propensity for recovery rates to affect tranche
prices; and
to the extent the comprehensive risk measure incorporates benefits from dynamic
hedging, the risk of hedging slippage and the potential costs of rebalancing such hedges.
[BCBS December 2010 par 718(xcv)]
In principle an integrated modelling approach is desirable. For the present, banks may adopt
approaches that capitalise different risks differently (eg via an add-on approach), provided
that this can be undertaken conservatively and it does not undermine the strength of risk
management. However, the capital charges calculated with the different models would have
to be added using a simple sum and banks are encouraged to develop an integrated approach
over time. Note that Banks are allowed to enhance the IRC model to comply with the
requirements for the comprehensive risk measure. However, they are not allowed to perform
a single calculation covering exposures subject to the IRC charge and exposures subject to
the comprehensive risk capital charge. Disallowing a single calculation has the effect of not
allowing any diversification between the portfolios.
211. The approach must meet all of the requirements specified in section 9.11.5.1 and
Appendix 9-IX. This exception only applies to institutions that are active in buying and selling
these products. For the exposures that the institution does incorporate in its internally developed
approach, the institution will be required to subject them to a capital charge equal to the higher of
the capital charge according to this internally developed approach and 8% of the capital charge for
specific risk according to the standardized measurement method. It will not be required to subject
these exposures to the treatment according section 9.11.5.1 (i.e., it must incorporate them in both
the value-at-risk and stressed value-at-risk measures).45 [BCBS December 2010 par 718(xcv)]
45 Institutions must still include correlation trading portfolio products in VaR and stressed VaR models for general
market risk and interest rate specific risk.
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212. For an institution applying this exception, it must
Have sufficient market data to ensure that it fully captures the salient risks of these
exposures in its comprehensive risk measure in accordance with the standards set forth
above;
Demonstrate (for example, through backtesting) that its risk measures can appropriately
explain the historical price variation of these products; and
Ensure that it can separate the positions for which it holds approval to incorporate them
in its comprehensive risk measure from those positions for which it does not hold this
approval.
[BCBS December 2010 par 718(xcvi)]
213. In addition to these data and modelling criteria, for an institution to apply this exception
it must regularly apply a set of specific, predetermined stress scenarios to the portfolio that
receives internal model regulatory capital treatment (i.e., the ‘correlation trading portfolio’).
These stress scenarios will examine the implications of stresses to (i) default rates, (ii) recovery
rates, (iii) credit spreads, and (iv) correlations on the correlation trading desk’s profit and loss.
The institution must apply these stress scenarios at least weekly and report the results, including
comparisons with the capital charges implied by the institutions’ internal model for estimating
comprehensive risks, at least quarterly. Any instances where the stress tests indicate a material
shortfall of the comprehensive risk measure must be reported to OSFI in a timely manner. Based
on these stress testing results, OSFI may impose a supplemental capital charge against the
correlation trading portfolio, to be added to the institution’s internally modelled capital
requirement. For further detail refer to Appendix 9-X: Stress testing guidance for the correlation
trading portfolio. [BCBS December 2010 par 718(xcvii)]
214. An institution must calculate this incremental risk measure and comprehensive risk
measure at least weekly, or more frequently if directed by OSFI. The capital charge for
incremental risk is given by a scaling factor of 1.0 times the maximum of (i) the average of the
incremental risk measures over 12 weeks; and (ii) the most recent incremental risk measure.
Likewise, the capital charge for comprehensive risk is given by a scaling factor of 1.0 times the
maximum of (i) the average of the comprehensive risk measures over 12 weeks; and (ii) the most
recent comprehensive risk measure. Both capital charges are added up. There will be no
adjustment for double counting between the comprehensive risk measure and any other risk
measures. [BCBS December 2010 par 718(xcviii)]
9.11.6. Backtesting
215. Institutions that apply modelled estimates of specific risk are required to conduct
backtesting aimed at assessing whether specific risk is being accurately captured. The
methodology an institution should use for validating its specific risk estimates is to perform
separate backtests on sub-portfolios using daily data on sub-portfolios subject to specific risk.
The key sub-portfolios for this purpose are traded-debt and equity positions. However, if an
institution breaks down its trading portfolio into finer categories (e.g. emerging markets, traded
corporate debt, etc.), it is appropriate to keep these distinctions for sub-portfolio backtesting
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purposes. An institution is required to commit to a sub-portfolio structure and adhere to it unless
it can demonstrate to OSFI that it would be appropriate to change the structure. [BCBS June
2006 par 718(xcvii), revised December 2010 par 718(xci-1-)]
216. Institutions must have in place a process to analyze exceptions identified through the
backtesting of sub-portfolios of specific risk. This process is intended to serve as the
fundamental way in which institutions correct their models of specific risk in the event they
become inaccurate. There will be a presumption that models that incorporate specific risk are
"unacceptable" if the results at the sub-portfolio level produce a number of exceptions
commensurate with the Red Zone as defined in the document, Supervisory framework for the use
of backtesting in conjunction with the internal models approach to market risk capital
requirements, issued by the Basel Committee on Banking Supervision in April 1996. Institutions
with “unacceptable” specific risk models are expected to take immediate action to correct the
problem in the model and to ensure that there is a sufficient capital buffer to absorb those risks
that backtests identify as being inadequately captured. [BCBS June 2006 par 718(xcviii), revised
December 2010 par 718(xci-2-)]
9.11.7. Stress testing
217. Institutions that use the internal models approach for meeting market risk capital
requirements must have in place a rigorous and comprehensive stress testing program. Stress
testing to identify events or influences that could greatly impact institutions is a key component
of an institution's assessment of its capital position. [BCBS June 2006 par 718(lxxvii)]
218. Institutions' stress scenarios need to cover a range of factors that can create
extraordinary losses or gains in trading books, or make the control of risk in those books very
difficult. These factors include low-probability events in all major types of risks, including the
various components of market, credit, and operational risks. Stress scenarios need to shed light
on the impact of such events on positions that display both linear and non-linear price
characteristics (i.e., options and instruments that have options-like characteristics). [BCBS June
2006 par 718(lxxviii)]
219. Institutions' stress tests should be both of a quantitative and qualitative nature,
incorporating both market risk and liquidity aspects of market disturbances. Quantitative criteria
should identify plausible stress scenarios to which institutions could be exposed. Qualitative
criteria should emphasize that two major goals of stress testing are to evaluate the capacity of the
institution's capital to absorb potential large losses and to identify steps the institution can take to
reduce its risk and conserve capital. This assessment is integral to setting and evaluating the
institution's management strategy and the results of stress testing should be routinely
communicated to senior management.
[BCBS June 2006 par 718(lxxix)]
220. Institutions should combine the use of supervisory stress scenarios with stress tests
developed by institutions themselves to reflect their specific risk characteristics. OSFI may ask
institutions to provide information on stress testing in three broad areas: [BCBS June 2006 par
718(lxxx)]
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a. Supervisory scenarios requiring no simulations by the institution
Institutions should have information on the largest losses experienced during the
reporting period available for supervisory review. This loss information could be
compared to the level of capital that results from an institution's internal measurement
system. For example, it could provide OSFI with the coverage ratio of reported VaR
capital to the maximum one day loss during the reporting period. [BCBS June 2006 par
718(lxxxi)]
b. Scenarios requiring a simulation by the institution
Institutions should subject their portfolios to a series of simulated stress scenarios and
provide OSFI with the results quarterly. These scenarios could include testing the current
portfolio against past periods of significant disturbance, for example the 1987 equity
crash, the Exchange Rate Mechanism crises of 1992 and 1993,the fall in bond markets in
the first quarter of 1994, the 1998 Russian financial crisis, the 2000 bursting of the
technology stock bubble or the 2007/2008 sub-prime crisis, incorporating both the large
price movements and the sharp reduction in liquidity associated with these events. A
second type of scenario would evaluate the sensitivity of the institution's market risk
exposure to changes in the assumptions about volatilities and correlations. Applying this
test would require an evaluation of the historical range of variation for volatilities and
correlations and evaluation of the institution's current positions against the extreme
values of the historical range. Due consideration should be given to the sharp variation
that at times has occurred in a matter of days in periods of significant market disturbance.
For example, the above-mentioned situations involved correlations within risk factors
approaching the extreme values of 1 or -1 for several days at the height of the
disturbance. [BCBS June 2006 par 718(lxxxii)]
c. Scenarios developed by the institution itself to capture the specific characteristics of its
portfolio
In addition to the scenarios prescribed by OSFI under (a) and (b) above, an institution
should also develop its own stress tests which it identifies as most adverse based on the
characteristics of its portfolio (e.g., problems in a key region of the world combined with
a sharp move in oil prices). Institutions should provide OSFI with a description of the
methodology used to identify and carry out the scenarios as well as with a description of
the results derived from these scenarios. [BCBS June 2006 par 718(lxxxiii)]
221. The results should be reviewed periodically by senior management and should be
reflected in the policies and limits set by management. Moreover, if the testing reveals particular
vulnerability to a given set of circumstances, OSFI would expect the institution to take prompt
steps to manage those risks appropriately (e.g., by hedging against that outcome or reducing the
size of its exposures). [BCBS June 2006 par 718(lxxxiv)]
9.11.8. Model validation
222. It is important that institutions have processes in place to ensure that their internal
models have been adequately validated by suitably qualified parties independent of the
development process and to ensure that they are conceptually sound and adequately capture all
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material risks. This validation should be conducted when the model is initially developed and
when any significant changes are made to the model. The validation should also be conducted
on a periodic basis but especially when there have been any significant structural changes in the
market or changes to the composition of the portfolio that might lead to the model being no
longer adequate. More extensive model validation is particularly important when specific risk is
modelled and the model is required to meet the additional criteria in section 9.11.5. As
techniques and best practices evolve, institutions should avail themselves of these advances.
Model validation should not be limited to backtesting, but should, at a minimum, also include the
following: [BCBS June 2006 par 718(xcix)]
a. Tests to demonstrate that any assumptions made within the internal model are appropriate
and do not underestimate risk. These may include the assumption of the normal
distribution, the use of the square root of time to scale from a one-day holding period to a
10-day holding period, the use of extrapolation or interpolation techniques, and the use of
pricing models. [BCBS June 2006 par 718(xcix)(a)]
b. Further to regulatory backtesting programs, testing for model validation must use
hypothetical changes in portfolio value that would occur were end-of-day positions to
remain unchanged. [revised BCBS December 2010 par 718(xcix)(b)] Such tests would
therefore exclude fees, commissions, bid-ask spreads, net interest income and intra-day
trading. Moreover, additional tests are required which may include, for instance:
Testing carried out for periods that are longer than required for the regular
backtesting program (e.g. 3 years). The longer time period would generally
improve the power of the backtesting, but a longer time period may not be
desirable if the VaR model or market conditions have changed to the extent that
historical data is no longer relevant.
Testing carried out using confidence intervals other than the 99 percent interval
required under the quantitative standards.
Testing of portfolios below the overall bank level.
[BCBS June 2006 par 718(xcix)(b)]
c. The use of hypothetical portfolios to ensure that the model is able to account for and
adequately capture particular structural features that may arise, for example:
When data histories for a particular instrument do not meet the quantitative
standards in section 9.11.4 and the institution has to map these positions to
proxies. In such a situation the institution must ensure that the proxies produce
conservative results under relevant market scenarios.
When material basis risks are present, which may include mismatches between
long and short positions either by maturity or by issuer.
When concentration risk (as would occur in an undiversified portfolio) is present.
[BCBS June 2006 par 718(xcix)(c)]
223. In addition, in reviewing an institution's internal model OSFI will require assurance that:
The internal validation processes described in section 9.11.2. are operating in a
satisfactory manner.
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The formulae used in the calculation process as well as for the pricing of options and
other complex instruments are validated by a qualified unit, which in all cases should be
independent from the trading area.
The structure of internal models is adequate with respect to the institution's activities and
geographical coverage.
The results of the institutions' back-testing of its internal measurement system (i.e.,
comparing value-at-risk estimates with actual profits and losses) ensure that the model
provides a reliable measure of potential losses over time. The results as well as the
underlying inputs to their value-at-risk calculations should be available to OSFI and
external auditors on request.
Data flows and processes associated with the risk measurement system are transparent
and accessible. In particular, it is necessary that auditors or OSFI are in a position to
have easy access, whenever they judge it necessary and under appropriate procedures, to
the models' specifications and parameters.
[BCBS June 2006 par 718(lxxxv)]
9.11.9. Combination of internal models and the standardized methodology
224. Unless an institution's exposure to a particular risk factor, such as commodity prices, is
insignificant, the internal measurement system will, in principle, require institutions to have an
integrated risk measurement system that captures the broad risk factor categories (i.e., interest
rates, exchange rates, equity prices and commodity prices, with related options volatilities being
included in each risk factor category). Thus, institutions that start to use models for one or more
risk factor categories will, over time, be expected to extend the models to all their market risks.
An institution that has developed one or more models will no longer be able to revert to
measuring the risk measured by those models according to the standardized methodology (unless
OSFI withdraws approval for those models). However, pending further experience regarding the
process of changing to a models-based approach, no specific time limit will be set for institutions
which use a combination of internal models and the standardized methodology to move to a
comprehensive model.
225. The following conditions apply to institutions using such combinations:
a. Subject to transitional arrangements, each broad risk factor category must be assessed
using a single approach (either internal models or the standardized approach), i.e., no
combination of the two methods will be permitted within a risk category or across the
institutions' different entities for the same type of risk.46
b. All criteria in chapter 9 will apply to the models being used.
c. Institutions may not switch from a model to the standardized approach unless OSFI
rescinds permission to use the model for capital adequacy purposes.
46 However, institutions may incur risks in positions which are not captured by their models, for example, in
remote locations, in minor currencies or in negligible business areas. Such risks should be measured according
to the standardized methodology.
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d. No element of market risk may escape measurement, i.e., the exposure for all the various
risk factors, whether calculated according to the standardized approach or internal
models, would have to be captured.
e. The capital charges assessed under the standardized approach and under the models
approach are to be aggregated according to the simple sum method.
[BCBS June 2006 par 718(lxxxvi)]
226. On a case-by-case basis, OSFI may permit short term transitional arrangements for
using a combination of internal models and the standardized approach for any risk across all of
an institution's operations. Approval of these temporary arrangements will be subject to:
a. the institution providing adequate internal controls that prevent switching of business
between legal entities to achieve the most advantageous capital charge,
b. the Superintendent imposing an additional capital requirement which may be amended
periodically depending on the circumstances of the transitional arrangements. The
additional requirement will terminate once the risk category is fully assessed under the
internal models approach, and
c. the institution entering into a formal undertaking to comply with the conditions of the
temporary arrangement and to expand the internal model on or before a specific date to
those operations initially using the standardized approach.
[BCBS June 2006 par 708(i)]
Appendix 9-9 - The Incremental Risk Charge
227. The incremental risk charge (IRC) set forth below is intended to complement additional
standards being applied to the value-at-risk modelling framework. As described in more detail
below, the IRC represents an estimate of the default and migration risks of non-tranched
products, with exposure to interest rate risk, over a one-year capital horizon at a 99.9 percent
confidence level, taking into account the liquidity horizons of individual positions or sets of
positions. This appendix provides guidelines on how an IRC model should be developed by
institutions for calculating the IRC for these positions. It also contains guidance on how OSFI
will evaluate institutions’ IRC models. [BCBS July 2009 – Guidelines for computing capital for
incremental risk in the trading book (henceforth BCBS July 2009 IRC) par (2)].
228. An institution has to meet the guidelines for calculating the IRC that are laid out in this
Appendix to the extent that it seeks to model incremental risks, as part of its interest rate specific
risk VaR model, section 9.11.5.1 or comprehensive risks according to section 9.11.5.2. [BCBS
July 2009 IRC par (3)]
II. Principles for calculating the IRC
A. IRC-covered positions and risks
229. The IRC encompasses all positions subject to a capital charge for specific interest rate
risk according to the internal models approach to specific market risk but not subject to the
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treatment outlined in sections 9.10.1.1 for tranched products, regardless of their perceived
liquidity. [BCBS July 2009 IRC par (8)]
OSFI Notes
230. Banks should include all sovereign debt positions in their IRC models.
231. With OSFI approval, a bank can choose consistently to include all listed equity and
derivatives positions based on listed equity of a desk in its incremental risk model. [BCBS July
2009 IRC par (9)]
OSFI Notes
232. At this time the OSFI is not confident in the ability of firms to model migration and
default risk in equities. In time, as modelling standards evolve the OSFI will revisit this policy.
In the context of convertible bonds, a bank could achieve partial hedge recognition by including
the embedded warrant component of this hybrid instrument in its equity general market risk VaR
and equity specific risk VaR models. If a bank elects to do this, at a minimum the remainder of
the decomposed convertible bond is still subject to default and migration risk, which should
either be captured in an IRC model or through the application of the standardized framework for
convertible bonds (see Sections 9.10.1 and 9.10.2).
233. Additionally, an institution is not permitted to incorporate into its IRC model any
securitization positions, even when securitization positions are viewed as hedging underlying
credit instruments held in the trading account. [BCBS July 2009 IRC par (10)]
234. For IRC-covered positions, the IRC captures
Default risk. This means the potential for direct loss due to an obligor’s default as well as
the potential for indirect losses that may arise from a default event;
Credit migration risk. This means the potential for direct loss due to an internal/external
rating downgrade or upgrade as well as the potential for indirect losses that may arise
from a credit migration event. [BCBS July 2009 IRC par (11)]
B. Key supervisory parameters for computing IRC
1. Soundness standard comparable to IRB
235. One of the underlying objectives of IRC is to achieve broad consistency between
capital charges for similar positions (adjusted for illiquidity) held in the banking and trading
books. Since the Basel II Framework reflects a 99.9 percent soundness standard over a one-year
capital horizon, the IRC is also described in these terms. [BCBS July 2009 IRC par (12)]
236. Specifically, for all IRC-covered positions, an institution’s IRC model must measure
losses due to default and migration at the 99.9 percent confidence interval over a capital horizon
of one year, taking into account the liquidity horizons applicable to individual trading positions
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or sets of positions. Losses caused by broader market-wide events affecting multiple
issues/issuers are encompassed by this definition. [BCBS July 2009 IRC par (13)]
237. As described immediately below, for each IRC-covered position the model should also
capture the impact of rebalancing positions at the end of their liquidity horizons so as to achieve
a constant level of risk over a one-year capital horizon. The model may incorporate correlation
effects among the modelled risk factors, subject to validation standards set forth in Section III.
The trading portfolio’s IRC equals the IRC model’s estimate of losses at the 99.9 percent
confidence level. [BCBS July 2009 IRC par (14)]
2. Constant level of risk over one-year capital horizon
238. An IRC model should be based on the assumption of a constant level of risk over the
one-year capital horizon.47 [BCBS July 2009 IRC par (15)]
239. This constant level of risk assumption implies that an institution rebalances, or rolls
over, its trading positions over the one-year capital horizon in a manner that maintains the initial
risk level, as indicated by a metric such as VaR or the profile of exposure by credit rating and
concentration. This means incorporating the effect of replacing positions whose credit
characteristics have improved or deteriorated over the liquidity horizon with positions that have
risk characteristics equivalent to those that the original position had at the start of the liquidity
horizon. The frequency of the assumed rebalancing must be governed by the liquidity horizon for
a given position. [BCBS July 2009 IRC par (16)]
240. Rebalancing positions does not imply, as the IRB approach for the banking book does,
that the same positions will be maintained throughout the capital horizon. Particularly for more
liquid and more highly rated positions, this provides a benefit relative to the treatment under the
IRB framework. However, an institution may elect to use a one-year constant position assumption,
as long as it does so consistently across all portfolios. [BCBS July 2009 IRC par (17)]
3. Liquidity horizon
241. Stressed credit market events have shown that institutions cannot assume that markets
remain liquid under those conditions. Banks experienced significant illiquidity in a wide range of
47 This assumption is consistent with the capital computations in the Basel II Framework. In all cases (loans,
derivatives and repos), the Basel II Framework defines EAD in a way that reflects a roll-over of existing
exposures when they mature.
The combination of the constant level of risk assumption and the one-year capital horizon reflects supervisors’
assessment of the appropriate capital needed to support the risk in the trading portfolio. It also reflects the
importance to the financial markets of banks having the capital capacity to continue providing liquidity to the
financial markets in spite of trading losses. Consistent with a “going concern” view of a bank, this assumption is
appropriate because a bank must continue to take risks to support its income-producing activities. For regulatory
capital adequacy purposes, it is not appropriate to assume that a bank would reduce its VaR to zero at a short-
term horizon in reaction to large trading losses. It also is not appropriate to rely on the prospect that a bank could
raise additional Tier 1 capital during stressed market conditions.
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credit products held in the trading book, including leveraged loans. Under these circumstances,
liquidity in many parts of the securitization markets dried up, forcing banks to retain exposures
in securitization pipelines for prolonged periods of time. Institutions must pay particular
attention to the appropriate liquidity horizon assumptions within their IRC models. [BCBS July
2009 IRC par (18)]
242. The liquidity horizon represents the time required to sell the position or to hedge all
material risks covered by the IRC model in a stressed market. The liquidity horizon must be
measured under conservative assumptions and should be sufficiently long that the act of selling
or hedging, in itself, does not materially affect market prices. The determination of the
appropriate liquidity horizon for a position or set of positions may take into account an
institution’s internal policies relating to, for example, prudent valuation (as per the prudent
valuation guidance of the Basel II Framework), valuation adjustments48 and the management of
stale positions. [BCBS July 2009 IRC par (19)]
243. The liquidity horizon for a position or set of positions has a floor of three months.
[BCBS July 2009 IRC par (20)]
244. In general, within a given product type a non-investment-grade position is expected to
have a longer assumed liquidity horizon than an investment-grade position. Conservative
assumptions regarding the liquidity horizon for non-investment-grade positions are warranted
until further evidence is gained regarding the market’s liquidity during systematic and
idiosyncratic stress situations. Firms also need to apply conservative liquidity horizon
assumptions for products, regardless of rating, where secondary market liquidity is not deep,
particularly during periods of financial market volatility and investor risk aversion. The
application of prudent liquidity assumptions is particularly important for rapidly growing product
classes that have not been tested in a downturn. [BCBS July 2009 IRC par (21)]
245. An institution can assess liquidity by position or on an aggregated basis (“buckets”). If
an aggregated basis is used (e.g. investment-grade European corporate exposures not part of a
core CDS index), the aggregation criteria would be defined in a way that meaningfully reflect
differences in liquidity. [BCBS July 2009 IRC par (22)]
246. The liquidity horizon is expected to be greater for positions that are concentrated,
reflecting the longer period needed to liquidate such positions. This longer liquidity horizon for
concentrated positions is necessary to provide adequate capital against two types of
concentration: issuer concentration and market concentration. [BCBS July 2009 IRC par (23)]
48 For establishing prudent valuation adjustments, see sections 9.8.3 and 9.8.4.
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4. Correlations and diversification
(a) Correlations between defaults and migrations
247. Economic and financial dependence among obligors causes a clustering of default and
migration events. Accordingly, the IRC charge includes the impact of correlations between
default and migration events among obligors and an institution’s IRC model must include the
impact of such clustering of default and migration events. [BCBS July 2009 IRC par (24)]
(b) Correlations between default or migration risks and other market factors
248. The impact of diversification between default or migration risks in the trading book and
other risks in the trading book is not currently well understood. Therefore, for the time being, the
impact of diversification between default or migration events and other market variables would
not be reflected in the computation of capital for incremental risk. This is consistent with the
Basel II Framework, which does not allow for the benefit of diversification when combining
capital requirements for credit risk and market risk. Accordingly, the capital charge for
incremental default and migration losses is added to the VaR-based capital charge for market
risk. [BCBS July 2009 IRC par (25)]
5. Concentration
249. An institution’s IRC model must appropriately reflect issuer and market concentrations.
Thus, other things being equal, a concentrated portfolio should attract a higher capital charge
than a more granular portfolio (see also paragraph 247). Concentrations that can arise within and
across product classes under stressed conditions must also be reflected. [BCBS July 2009 IRC
par (26)]
6. Risk mitigation and diversification effects
250. Within the IRC model, exposure amounts may be netted only when long and short
positions refer to the same financial instrument. Otherwise, exposure amounts must be captured
(and modelled separately) on a gross (i.e. non-netted) basis in order to reflect basis risk in the
model. Thus, hedging or diversification effects associated with long and short positions
involving different instruments or different securities of the same obligor (“intra-obligor
hedges”), as well as long and short positions in different issuers (“interobligor hedges”), may not
be recognised through netting of exposure amounts. Rather, such effects may only be recognised
by capturing and modelling separately the gross long and short positions in the different
instruments or securities. [BCBS July 2009 IRC par (27)]
251. Significant basis risks by product, seniority in the capital structure, internal or external
rating, maturity, vintage for offsetting positions as well as differences between offsetting
instruments, such as different payout triggers and procedures, should be reflected in the IRC
model. [BCBS July 2009 IRC par (28)]
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252. If an instrument has a shorter maturity than the liquidity horizon or a maturity longer
than the liquidity horizon is not contractually assured, the IRC must, where material, include the
impact of potential risks that could occur during the interval between the maturity of the
instrument and the liquidity horizon. [BCBS July 2009 IRC par (29)]
253. For trading book risk positions that are typically hedged via dynamic hedging strategies,
a rebalancing of the hedge within the liquidity horizon of the hedged position may also be
recognised. Such recognition is only admissible if the institution:
a. chooses to model rebalancing of the hedge consistently over the relevant set of trading
book risk positions,
b. demonstrates that the inclusion of rebalancing results in a better risk measurement, and
c. demonstrates that the markets for the instruments serving as hedge are liquid enough to
allow for this kind of rebalancing even during periods of stress.
254. Any residual risks resulting from dynamic hedging strategies must be reflected in the
capital charge. An institution should validate its approach to capture such residual risks to the
satisfaction of OSFI. [BCBS July 2009 IRC par (30)]
7. Optionality
255. The IRC model must reflect the impact of optionality. Accordingly, institutions’ models
should include the nonlinear impact of options and other positions with material nonlinear
behaviour with respect to price changes. The institution should also have due regard to the
amount of model risk inherent in the valuation and estimation of price risks associated with such
products. [BCBS July 2009 IRC par (31)]
III. Validation
256. Institutions should apply the validation principles described in the Basel II Framework
in designing, testing and maintaining their IRC models. This includes evaluating conceptual
soundness, ongoing monitoring that includes process verification and benchmarking, and
outcomes analysis. Some factors that should be considered in the validation process include:
Liquidity horizons should reflect actual practice and experience during periods of both
systematic and idiosyncratic stresses.
The IRC model for measuring default and migration risks over the liquidity horizon
should take into account objective data over the relevant horizon and include a
comparison of risk estimates for a rebalanced portfolio with that of a portfolio with fixed
positions.
Correlation assumptions must be supported by analysis of objective data in a
conceptually sound framework. If an institution uses a multi-period model to compute
incremental risk, it should evaluate the implied annual correlations to ensure they are
reasonable and in line with observed annual correlations. An institution must validate that
its modelling approach for correlations is appropriate for its portfolio, including the
choice and weights of its systematic risk factors. An institution must document its
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modelling approach so that its correlation and other modelling assumptions are
transparent to supervisors.
Owing to the high confidence standard and long capital horizon of the IRC, robust direct
validation of the IRC model through standard backtesting methods at the 99.9%/one-year
soundness standard will not be possible. Accordingly, validation of an IRC model
necessarily must rely more heavily on indirect methods including but not limited to stress
tests, sensitivity analyses and scenario analyses, to assess its qualitative and quantitative
reasonableness, particularly with regard to the model’s treatment of concentrations.
Given the nature of the IRC soundness standard such tests must not be limited to the
range of events experienced historically. The validation of an IRC model represents an
ongoing process in which supervisors and firms jointly determine the exact set of
validation procedures to be employed.
Firms should strive to develop relevant internal modelling benchmarks to assess the
overall accuracy of their IRC models.
[BCBS July 2009 IRC par (32)]
IV. Use of internal risk measurement models to compute the IRC
257. As noted above, these guidelines do not prescribe any specific modelling approach for
capturing incremental risk. Because a consensus does not yet exist with respect to measuring risk
for potentially illiquid trading positions, it is anticipated that institutions will develop different
IRC modelling approaches. [BCBS July 2009 IRC par (33)]
258. The approach that an institution uses to measure the IRC is subject to the “use test”.
Specifically, the approach must be consistent with the institution’s internal risk management
methodologies for identifying, measuring, and managing trading risks. [BCBS July 2009 IRC par
(34)]
259. Ideally, the supervisory principles set forth in this Appendix would be incorporated
within an institution’s internal models for measuring trading book risks and assigning an internal
capital charge to these risks. However, in practice an institution’s internal approach for
measuring trading book risks may not map directly into the above supervisory principles in terms
of capital horizon, constant level of risk, rollover assumptions or other factors. In this case, the
institution must demonstrate that the resulting internal capital charge would deliver a charge at
least as high as the charge produced by a model that directly applies the supervisory principles.
[BCBS July 2009 IRC par (35)]
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Appendix 9-10 - Stress testing guidance for the correlation trading portfolio
1. Introduction
260. The Revisions to the Basel II market risk framework permit banks meeting certain
conditions to calculate specific risk capital charges for the correlation trading portfolio (CTP)
using a comprehensive risk modelling (CRM) approach. One of these conditions is that an
institution using the CRM approach must conduct, at least weekly, a set of pre-determined stress
tests for the CTP encompassing shocks to default rates, recovery rates, credit spreads, and
correlations. This Appendix provides guidance on the stress testing that should be undertaken to
satisfy this requirement. [BCBS December 2010 Annex par (1)]
2. Overview
261. The goal of the stress testing standards described below is to provide estimates of the
mark-to-market (MTM) changes that would be experienced by the current CTP in the event of
credit-related shocks. The standards encompass both prescribed regulatory stress scenarios and
high-level principles governing an institution’s internal stress testing. The prescribed scenarios
are not intended to capture all potential sources of stress. Rather, their primary focus is on
valuation changes involving large, broad-based movements in spreads for single name bonds and
credit default swaps (CDS), such as could accompany major systemic financial or
macroeconomic shocks, and associated spillovers to prices for index and bespoke tranches and
other complex correlation positions. In addition to the prescribed scenarios, an institution is
expected to implement a rigorous internal stress testing process to address other potential
correlation trading risks, including institution-specific risks related to its underlying business
model and hedging strategies. [BCBS December 2010 Annex par (2)]
3. Prescribed stress tests
262. The prescribed stress scenarios below are framed in terms of risk factor movements
affecting credit spreads over specific historical reference periods. The term ‘risk factor’
encompasses any parameter or input within the pricing model that can vary over time. Examples